What kind of training are you doing? Are you following a certain group/person?
If you aren’t, you might want to check into Parelli. They have some youtube videos and do a lot with horses who get bored very easily.
With the gate thing, does he buck when you ask him to move away? My horse does the same thing around gates. I just make him work harder near the gates when he tries to stop. And like your horse, mine only does it when in the arena and saddled.
Have you tried doing other things in the arena besides doing circles or jumping? Maybe find a place that has arena trails, cows, etc. My friend’s TB loves cow work. I would continue to try new things with him, but make him work hard when he goes to the gate or even moves towards his pen.
“make the wrong thing hard and the right thing easy”
Good luck. Having a green horse is a learning and growing experience for both human and horse. I know I’m learning a crap ton of stuff with my new boy too. and it can be very frustrating at times, but so worth it in the end.
"Take the time it takes, so that it takes less time."
"Expect a lot, accept a little, reward often."