What resources, schemes, and strategies does a medieval king need to protect their power without killing or torturing?
Location location location. Make yourself such a hard target no one wants to attack you.
The problem with an army is that they come from the population, especially in medieval times. Losing too much of your army means you lose the war, and even if you "win" the impact on your country can be so large that you choose not to fight certain targets.
Switzerland managed to stay out of both world wars despite being smack in the middle of Europe because it was surrounded by mountains, it's army was trained for the region but the other armies had to worry about training for many other types of environment. On top of that all entrances into the country could either be destroyed or so easily defended you could swallow an army with a small force before they were breached.
Your king's lands have many powerful natural borders that are easily defended and nigh impossible to cut off from supplies and reinforcements. Anyone who would claim victory against you would have to deplete the manpower of a much larger kingdom and leave themselves open to attack from their neighbours from the moment you gather your troops at the border.
You can then add other safeguards. Your country might be a vital trade-route, and if you simply close your borders to any of them the economic impact could be large. Diplomacy could help secure your borders as declaring war on you means fighting a war in two fronts.
It's just too damn expensive to attack you and it will likely cause the attacking kingdom to fall shortly after an unlikely victory on you. So why bother?
Open thy gates!
When the Norsemen invaded France, a king just gave them Normandy. When the Dane conquered York, they stayed. But a mere two generations later, they were of a different culture, had adopted and adapted to the lands they took... In some ways, the culture of the losing side conquered the invader!
When The Yuan Dynasty established itself, the illustrious emperor Kublai Khan at times would (re?) integrate regional lords without a single person dying, while those resisting were made examples.
In other words: Surrender is an option to save a whole country's population. Any overlord worth his salt will not uproot a whole region to plunder and sack them and destroy the whole leadership there, if they pay their tributaries and taxes on time.
Now, take that, turn it to 11 and you get Ankh Morpork (thanks to the late Sir Terry Pratchett OBE): invasions are met with open doors and discount offers to the new overlords... And some days later the organized army has turned into a bunch of disconnected, unarmed people in rags.
No enemies had ever taken Ankh-Morpork. Well technically they had, quite often; the city welcomed free-spending barbarian invaders, but somehow the puzzled raiders found, after a few days, that they didn't own their horses any more, and within a couple of months they were just another minority group with its own graffiti and food shops.
Terry Pratchett: Eric; Discworld #9
Also Note, that Terry Pratchett's Ankh Morpork runs on an extreme form of Laissez-Faire Capitalism with little to no intervention by the de-facto ruler or the proper ruler.
You control access to a very precious resource and can destroy it if you're attacked (a very deep mine that could collapse, some kind of plant you could burn,...). People that want that resource and currently trade it with you would be very sad if that resource went to disappear. It will have both the effect of making people less likely to attack you AND create some allies/trade partners very likely to defend you (you won't kill anyone... but they might ?).
Simply have a very powerful ally for any reason. People won't attack you if they risk getting stomped by your friend.
Be completely uninteresting. Your kingdom present no advantage whatsoever to anyone.
Be hard to attack. See @Demigan answer.
Any combination of these (except 1 and 3... obviously).
You would need mind control or other mind-targeting tactic such as heavy propaganda. Even if the king does not really resort to violence, it is necessary to build a fearsome reputation. Alternatively, have allies that will defend the king, but I don't think you want that either.
Reason: If you need to "defend" against something, then there are only two outcomes- peaceful or bloody resolution. Obviously, you don't want the bloody one, so anyone that wants to fight will have to be pacified in some way (through "peaceful" methods).
You reach a mutually beneficial agreement. An amicable method. Not always available.
You intimidate the enemy into submission. Your reputation is fearsome enough that the enemy thinks they cannot possibly win a confrontation. They give up.
Now, eventually you'll run into someone who doesn't care about your reputation, because they're suicidal or they have nothing to lose. So the above method is not a surefire way.
The only sure way I can think of is having an impenetrable barrier that will never be broken, and then just arresting and exiling the troublesome one outside the walls. To do this, you need overwhelming strength and technology to subdue bloodlessly and ensure the walls won't be broken. You can save the technology if you just jail all dissidents and put them through a program that will reform them.
Also, you can combine the two methods.
Without overwhelming might, your king doesn't have the right to be so idealistic and naive.
Tactics of the scorched earth
This heavily depends on some conditions.
You don't always look weak when not actively engaging your enemy. You can defeat people without lifting a finger. As an easy example, don't attack Russia in winter.
Your king and subjects can have the advantage of braving a hostile land. A desert, mountains, extremely cold regions like can give this advantage. All you need to do is walk away when they come, taking as much resources with you as possible. They will endure a harsh, unforgiving environment. Not encountering enemies and only empty cities with little food and/or water will not make them happy. The supply lines will get harder, as they need to go further away through an inhospitable environment as well. They will respect the king for it, as he and his people are well organized to do this as well as able to live in the harsh land. The king or his subjects do not kill. The enemy has all the ability to know when they are taking risks for their armies. They are the ones responsible.
This could conceivably be done in more normal environments. Simply retreating with as much cattle and resources as you can. Burn the crops. Poison wells (Allowed if they know it's poisoned?). Hide and retreat. Remove the food and valuables and just let them come.
In a less harsh environment this might not lead to direct deaths, but this can demoralise the enemy. At first they might think they are doing a good thing, as they can take empty villages and cities, but it'll turn sour as they notice it's everywhere. No battles to win. No proxy battles or the like. Just endless walking. The only food coming from the supply lines, which is a very expensive thing and possibly not enough the further you go into enemy territory. As you don't meet anyone, you might be extra cautious with your army and supply lines as well.
And what will happen if you "conquer" the capital city? Nothing. You have no one to give orders to. No one to pressure to do your bidding. The people will go back to their houses and ignore you, even if you can find them. Torching their homes, killing anyone you see or whatever isn't helping.
The people join this tactic, as it'll make for less death and destruction than engaging. They know that some can starve, be captured and killed. That they will face difficult times. But they are used to it. They can weather it. They praise their king and no one else. The only way to defeat them is to try to kill them all and occupy their houses with your own people. Some armies might be prepared to kill a whole city, but if this is done one after the other, possibly after a long game of cat and mouse, many will feel horrified at their doings.
Simply not engaging the enemy, ignoring them or run away with your stuff, can make most enemies falter. This is extra helpful if the environment is very harsh and you're the only one used to this. The enemy will die, disband or just return relatively empty handed. Only with special tactics and extreme measures you might defeat these people and their king, but even dishonerable people will go only so far. Indeed, the effort to take them on is likely seen as so much, they might not even try any more, or be able to convince their armies to start an attack on the country.
You are right that a "good" king might be seen as weak, but if he or she can manage to be seen as "enlightened" instead, there could be benefits for the kingdom, the population, and hence the king. Would you want to be the ruler of a pit of vipers, or the merely first-among-equals in a much larger pond?
- It is generally understood that a free, democratic, and capitalist society does outcompete an autocracy. The devil is in the details, of course -- the rule of law seems to be much more important than true democracy, at least on the short run.
- A king who gets into the habit of torturing opponents might also torture those who give true but unpalatable advice.
Kings who resort to torture too quickly don't have a successful reign. Smart subjects understand that.
The inital part of the question was removed, so this is no longer quite as relevant:
Your deliberately obscure style of prose (a bad fit for this site, BTW) has obscured some truths. Let's start at the beginning:
- Evolution has found it survival-positive for group members to engage in altruistic patterns. Should I take a risk to the propagation of my own genes if that risk greatly enhances the propagation chances of my siblings? How about my cousins?
- It can be a workable negotiation strategy to appear like a madman, easily triggered into a mutually destructive frenzy.
- Do you remember how the Vietnamese defeated the mighty United States? Yes, I wrote "defeated" and I mean it in this context. The Communist forces were willing to raise the stakes to a point where the United States was no longer willing to pay the price for victory. The United States could have won, but they were unwilling to take the (comparatively much lower) losses any more. That's defeat.
Internal and external threats The Kingdom must Counter threats from within and the outside threats from within come in the form of barbarians neighboring nations And would be empires. Internal threats come from Rebellions not peasants rebellions as in most cases peasants are too busy starving to actually form and organize rebellion. However rogue family members and scheming noble houses Do quite well at starting Rebellions.
Be small. This will help with the internal threats and since you don't have an army said you can't kill there's really no need to be big as one of the main benefits and being big is to get a larger army. Been small make you less threatening And means you have less vassals who can rebel against you.
Invest in a trade Empire.
Sent you can't focus on armies or In secret police, Invest in trade try to get your neighbors economically dependent on you this will make them less likely to invade as they might inadvertently destroy their own economy. Don't hoard the wealth though see that it's distributed well between your fellow aristocrats and merchants. As much as possible get them to compete with each other for trade deals. This will discourage The unity needed for rebellion and will ensure that everyone's too busy making money to contemplate plans of disrupting The status quo.
- Marriage alliance. Now that you have a trade Empire you need lots of kids the prefirmly daughters, You gonna have to Use most of that wealth to seek secure alliances with several neighboring countries with large armies. You can use these alliances to Discourage enemies who might see your lack of armies as easy Prey. It would also discourage armed rebellion for the same reason though you don't have an army your son-in-law's do and they have already agreed to help you.