I never experienced stuff like that, especially Trico getting stuck or spinning around, and I'm currently on a second playthrough
The last one is debatable.
I agree. I would even say that for how the game is structured you don't really need Trico to do complex stuff. For most of my playthrough he progressed through the area naturally with few inputs to begin with. Some people seem hell-bent on this broken AI thing and I won't be able to change their mind but this is my experience with the game and hope that alleviates some issues they might have.
Most of the time he just needs a little positioning help and you can do everything with a simple R1 push in the spot you need him to stand
Sometimes, for jumps, he needs more space and you might have to call him back a bit so he can gain momentum and then press forward one time to let him do his thing.
It can get a bit more tricky when you need to put his tail somewhere specific but most of the time you can drag it yourself so his positioning doesn't need to be perfect.
For platforming sections you need to follow his eyes and point the direction one time at the start, he will complete the sequence by himself. If it's a long sequence, you might have to repeat the command one other time halfway but absolutely not for every jump
Don't issue commands when you are on top of his head, he lowers it and interprets it as a coddling gesture. If I put my hands on my dog's head and keep it there he does the same lol. But you can give a command from his back and when he's in position climb his head to reach your destination. Issue Commands always from standing position on his back or when you are on the ground.
In small environments he might try to follow you and adapt a stance not ideal for big movements such as jumps so you might have to lead him back to an open room and then re-enter, but it's very rare
I think you can finish the game simply using R1 and R1 plus forward, the other commands are used sparingly at most and even if it's a jump Trico for me reacted even with just pressing forward but ymmv in this case
Don't spam commands. Ever
That's mostly it. Hope my experience can alleviate some issues you might have.