I prefer to ride young horses alone so they learn to ride alone and gain confidence and trust in me. The more you ride him out and about the more relaxed he will get. A horse gets broke by putting hundreds of miles under their feet, outside the arena. As far as the gate I would get off and send him through it back and fourth until he walks through quietly, then ride him through. You can also put his feet to work near the gate with lots of changes of direction and make walking thorough the gate the easy thing to do. Be safe.
He is learning everyday but its that one gate he refuses to go through. I took him through a gate going from field to field, then a gate going out onto a trail; no problems. It's just the gate going back to the barn. From previous experiences with other greenies he should be very willing to go back to the barn, that means the work is done for now!
Sit tall in the saddle, hold your head up high, keep your eyes fixed where the trail meets the sky, & live like you aint afraid to die, & don't be scared, just enjoy your ride.