It seems to me that your future infantrymen will have access to Pulse Energy Projectile (PEP) lasers. If so, let's examine how these weapons would be deployed, employed, their effects, and their limitations. All of these will have effects on your primary questions.
Energy source aside - and unless your universe has some wonderous, handwavium metamaterials - Directed Energy Weapons like the PEP are generally heavy and bulky. This is because it requires a lot more components for it to generate a shot than current technology projectile weapons (we're not talking about miniature mass accelerator a la Mass Effect here). As such, even at the infantry level, these weapons will either be mounted on tripods to be carried around by its crew (hence the moniker 'crew-served weapons') or mounted on vehicles.
Only the PHaSR (Personnel Halting and Stimulation Response Rifle developed by the USAF; yes they actually called it that because of course) is somewhat man-portable, and that's a non-lethal, non-PEP device.
So for your PEP, I think the most realistic way it would be deployed is at the Platoon level as a specialized support weapon, either by a crew on a tripod, or mounted on vehicles. Everyone else will still use projectile weapons (advanced ones, of course, but essentially the rifles and machine guns we have today).
Onto your questions.
The effects of your PEP on the battlespace.
According to the literature I read, the PEP 'involves the emission of an invisible laser pulse which, upon contact with the target, ablates the surface and creates a small amount of exploding plasma.' (this is per Wikipedia, so keep that in mind I guess). While current technology PEPs are meant to be non-lethal, it's easy to see that if you scale this up, you can use PEPs to disable and/or destroy all manner of things that can be disabled and/or destroyed through exploding plasma. This includes vehicles (as they are currently looking at developing a counter-UAV PEP), buildings, etc.
Basically, the PEP is a very fast, long-range weapon that fires explosive projectiles without the kinetic energy transfer at the target. So if you fire a PEP at people hiding behind, say, a brick wall, well the wall will explode like its hit by - say - a 30mm shell (this is pure conjecture, by the way. I failed to locate sufficient data on how powerful the PEP plasma explosions are). The PEP projectile will not, of course, penetrate the wall, but shrapnel from the wall exploding might ruin their day, so it balances out.
The advantages of this system are that the projectiles travel at the speed of light; the PEP gunner no longer has to incorporate a lead to his aiming solutions for moving targets. The projectiles also travel in a straight line over long distances. Current technology PEP is effective up to 2km. This means that there is no ballistic drop for the gunner to compute and offset to as well. Basically, within its effective range, you can hit what you are aiming at almost instantaneously with an explosive projectile. That's an attractive thing for grunts.
Edited to add: The PEP is also an excellent point air defense system against missiles and low-flying aircraft. The PEP's advantages outlined in the paragraph above makes it an ideal system of choice - especially coupled with an automatic/autonomous target tracking and engagement guidence system like the AEGIS in US Navy ships.
There are several disadvantages as well: Laser Pulses can be dissipated through smoke/fog. Adversary forces will develop special counter-laser smoke grenades (say, containing particulates that reflect and/or disrupt the pulses) that their infantry can deploy to basically negate the effects of your weapon on target. Unlike physical projectiles which can punch through the smoke like nobody's business, that PEP projectile will just stop at the smoke. Funny thing about war is, the countermeasure is almost always cheaper than the systems they are designed to counter. So your PEP crew served might cost you USD 1.5 million per unit, while that smoke grenade probably costs the adversary USD 150 a pop. That's a bargain. Grunts love that too.
They are also heavy and bulky. A PEP team would consist of a gunner, an assistant gunner to set up and load the weapon, and an ammunition man to carry extra batteries, ammunition (whatever your PEP uses for ammo), etc. If they move, the gunner will hump the PEP gun, the a-gunner will hump the tripod, the ammo guy will hump his rucksack. Add to their loads their armor, personal weapons, supplies, etc. That is not a happy team. That is also not a fast team.
2. High ground
Well, since there are no ballistic calculations necessary for the PEP, then the high ground will have no effects on the PEP - other than if you're stupid enough to silhouette yourself on the crest of a hill, some guy with a PEP 2km away might take a potshot at you.
3. Collateral Damage
The PEP is highly accurate. You hit what you are aiming at. While the nature of the explosion can potentially cause collateral damage (exploding walls or vehicles, you know), the chances of it hitting something the gunner isn't aiming at is negligible at best.
This means that if you have to talk to the village elder to apologize about that goat that your PEP laser exploded, then your gunner was aiming at the goat.
4. Explosive Objects
I'd imagine that since the PEP creates exploding plasma on the target, then if the target is explosive, it would explode.
5. Small enclosed area
Well, two ways to see this. One, unlike traditional explosive projectiles, the PEP projectile itself does not generate fragments. So firing a PEP projectile into a room through a window, for instance, will just cause the PEP projectile to generate exploding plasma at whatever wall, object, or person it hits. The effect on the room is dependent on what object it hits. If it hits your buddy, you'd probably be covered in blood. You'd be unhappy, of course, but you'll generally be fine. On the other hand, there is that secondary effect. You fire a PEP projectile into the room, aiming for the back wall. When it hits that wall, it explodes, taking chunks of the wall with it, probably showering the occupants of the room with sharp brick fragments. The level of dismay and anger directed at you by the occupants of that room is directly proportional to the level of protection/armor they were wearing at the time.
The Effects of the PEP on Soldiers
As we have established above, the PEP is a support weapon. A highly specialized support weapon among other support weapons in the company. Remember: the PEP fires straight. This means that you can't use it for indirect support. It also doesn't have any kinetic energy, you can't use it to punch through walls or armor. It will, however, ablate armor and create plasma explosions, which you can use to disable or destroy vehicles, walls, etc. Combined with its lightspeed projectile and flat trajectory, the PEP is a pretty decent support weapon.
However, to gauge its effect on infantry equipment and tactics, several things must be considered.
Here's how you design infantry armor: You figure out what the most casualty-inducing weapon on the battlefield is, then you design armor that lowers the risk to your infantry to acceptable levels. Note that I did not say 'protects your infantry against this threat.' That is because this is impossible to do (unless we're talking about HALO/WH40K level power armors here).
Armor has to balance protection and mobility. Safety and comfort. The more comfortable your guys are, the longer they are combat effective. Add mobility, reduce protection and vice versa. Up to as recently as the late 90s, artillery is still the number one infantry killer. As such infantry armor up to the 90s was designed primarily against this threat (see the PASGT system for US Forces, for instance).
It is only when the US started to get into all these fights with guys who generally only have small arms and not a lot of artillery that the focus of armor shifted, somewhat, to defeat direct fire ballistic threats (with the development of the BALCS/SPEAR system for SOF troops, that trickled down to GPF troops later on for instance. And the SAPI/ESAPI ballistic plates of today).
Back to your question, having established that the PEP laser is a specialized support weapon, and, due to its limitations, most other weapons are still ballistic in nature (from bullets to artillery shells), then the armor your troops wear will be designed to defeat those threats. A combination of soft armor to defeat fragments and pistol caliber bullets, and hard armor plates to defeat rifle rounds. So, no change there.
There will be individual, vehicular, and area counter-laser systems, though, such as the smoke dispenser/grenade we discussed earlier. Or maybe some reflective panel add-ons to vehicle armor.
2. Suppression tactics.
This is where the PEP's rate of fire comes into play. You don't have to have a fully automatic system to suppress. You just need something that can fire accurately enough (no problems for the PEP), and quick enough to render the enemy combat ineffective within its beaten zone. If you can fire PEP lasers fast enough to keep the enemy from going anywhere and/or doing anything effective to you, then you're suppressing him. If not, then you're not. In any case, suppressing an enemy with direct fire weapons (which is what the PEP is), is pretty much that. It's really quite similar with suppressing the enemy with your carbine. Except that the PEP generates plasma explosions on the enemy's cover. Probably negating it after a while like hitting them with explosive projectiles.
The enemy will try to suppress your PEP crews like they would your other support weapons too. So, again, not a whole lot of difference.
The PEP wounds by a pressure wave that stuns the target and knocks them off their feet, and electromagnetic radiation that affects nerve cells causing a painful sensation. (again, Wikipedia). You scale this enough, then I suppose you have overpressure wounds and burns on human targets.
Can the PEP be a sniping weapon? Well, yes. It hits stuff it's aimed at 2km away, that's precise enough to be used to snipe folks. Is it practical? No. It's a support weapon. This is not to say that no one has ever sniped with support weapons before. As we discussed, it is heavy and cumbersome. So no sniping PEPs, at least none that was designed to do specifically that.
On the other hand, PEP crews are prime sniper targets - as support weapon crews generally are. Support weapons are force multipliers. Taking out its crew at critical points in a battle may very well change the course of the fight.
So TL;DR: Your PEP is a specialized support weapon because it's not practical enough to be man-portable, and it is inadvisable to replace the versatility and simplicity of projectile weapons on the battlefield.