this is the internet, and not seeing your bike in front of me makes it impossible to really see what is up, but a fd doing what you are describing doesn't make sense. Falling off the edge of the big ring means its the limit adjustment, not shifting onto the big ring is usually limit screw again or user error.

basically a fd is pretty simple in what it does and even I have set up new fd's on my bikes with no issues, with triples, and its pretty simple.
Either the bike has been dropped onto something and the fd has been bent or there are/is adjustment issues.
Any bike mechanic would see and fix the adjustment issues in a minute, so there are things here that don't make sense.

also, the fact that its a sora fd and the bike is 10 speed is of no consequence, all the fd does is to push the chain here or there, it needs to positioned on the frame properly and told where to "limit" its movement by the limit screws, the rest is pretty straightforward, especially with a simple friction setup like this bike has.