In a world where human and dinosaur co-exist, would it be a good idea to use dinosaur as a mount ?
More specific questions :
behavior wise it is impossible to say which can be domesticated as Upper pointed out. We can't measure how aggressive a fossil was. What really determines what is domesticated is what can be domesticated, llama are terrible pack animals but they were the only thing available to the Inca, so that is what they used. But the big factors like temperament, breeding behavior, and other behavior leave no fossil evidence so we have no idea.
Now assuming you can just say yout dinosaur has the right temperament, we can say anatomically which would be more useful if domesticated. There are some key traits you want in a pack/riding animal.
Herbivores generalist (or possibly omnivores like dogs), it needs to be easy to feed, you want to be able to feed it a wide variety of plant fodder otherwise it is useless for traveling. Grazers for preference, since grass is a lot easier to harvest.
breed quickly, if it takes too long to breed it is all but impossible to domesticate. You want many generations per generation of human, that rules out some of the larger sauropods.
Quadrupedal, while it is true some bipedal animals can be ridden, they can not carry people long distances and are useless for carrying cargo. You have to be really careful about distributing weight on a biped, quadruped animals are more forgiving. You also have the issue the only place you can sit or place cargo on a biped is right over the hips.
Herding, this is seen in every domesticated animal, sociality is a basic need for domesticated animals. It makes penning, breeding, and working with possible.
This leaves you with only a few groups, ceratopsians, large ornithopods (smaller ones are often bipedal), or small sauropods. Although larger ankylosaurs might be an option, we don't know if they are social.
lets look at each of them
Ceratopsians probably give you the greatest range of sizes, and they could be fitted with a saddle easily enough. Roughage diet which is good. No real downside.
Ornithischians appear to have spines along the back, so making a saddle would be tricky, on the other hand we know some are great distance travelers with migratory distances as high as any cursorial animals alive. There are many variations and plenty of grazers among them to pick from. good pack animal (sling packs), but tricky to ride.
Small sauropods are still huge and would be great for large loads especially if you stick to good roads. Big does make for slow breeding and training, they are also harder to feed since they are browsers. Probably not a good choice for anyone but royalty that can afford to feed them.
Ankylosaurus are slow but strong. They are bulk feeders meaning you can feed them damn near anything, plus the spines are mostly horizontal which makes it easy to pull a plow or wagon (they literally have built in yolks). Not great for riding though, very wide, you could build a chair like saddle however. Possibly solitary which is bad, but this is disputed and many not be universal in the group.
So you have your pick of those four groups.
Maybe. We obviously don't have dinosaurs to compare to, but their living descendants (birds) offer many examples of tamed or trained species. Chickens are thoroughly domesticated, and there are relatively tamed ostriches that you can ride. Falcons have been trained to hunt for centuries.
Of course, that's only a loose guide to dinosaurs themselves, and ability to be domesticated is something we don't have any examples of in dinosaurs proper. We have domesticated horses, but not zebras. It also matters what you mean, specifically, by domestication. Stuffing elephants full of opium has worked well enough to make them docile for riding.
Probably impossible to answer. Purpose is important: a large tetrapod might be good for hauling things, but might not be good for running down fast-moving prey. It also matters how readily they take to domestication. A docile vegetarian represents lower stakes if the domestication goes poorly, while a velociraptor might be harder to deal with (whatever the recent Jurassic Park movies suggest).
This also depends on the specific dinosaur. But generically, make a fitted saddle and harness, put it on the dinosaur, then climb up and direct it with whatever signals you've trained it to respond to (knee movements, a crop, reins, or whatever).
It depends on what you want the dinosaur to do for you, and how easy/safe they are to domesticate and train compared with other options like horses or mechanical devices.
As above, you will be hard pressed to find an experienced dinosaur trainer to tell you how docile they are. ;-) But that also means that nobody will be able to prove you wrong whatever you choose to assume on the subject.
We have domesticated some carnivores (cats and dogs), a number of herbivores (horses, donkeys, cows/oxen, elephants, etc.) and birds (notably falcons and pigeons have been very useful). Bigger and stronger dinosaur replacements for any of these would be interesting. It's impossible to say what would work: hippos and rhinos are apparently very bad tempered and impossible to tame. Horses and donkeys work, zebras don't. Pick what you want and use it. If you are interested in such details, a large domestic carnivore could be expensive to feed. You would need a society that has a surplus of meat products if you had domesticated large carnivores in number.
Riding a dinosaur depends a bit on what you are trying to accomplish. Generally, using muscles other than your own has been a good strategy throughout history. In times of war being on top of something big and strong is an advantage. Absolutely go for it if it works in your story.
Mounting and riding depends on the species. For two-legged species something like the tauntaun saddle in Star Wars looks believable to me. Bigger dinosaurs could accommodate a howdah.
Riding pterosaurs probably wouldn't work. People are up around the maximum carrying capacity of even the largest pterosaurs. It's unlikely they could carry a human any significant distance. Bird saddles don't seem practical. I think you'd have to go for a sack of some kind that is slung underneath. Takeoff is a problem. Still, people like to dream. If you aren't worried about being 100% realistic, you could fudge it. Many people have. Myself, I'd stick to things that are actually doable.
