You found the right site we have a bunch of FL350 gurus that will help you out they have seen or worked through about every problem you could ever have with a 350, they will be along shortly to reply I am sure.
I cant help you on the price but looking at the one pic I don't see a lot of value their with the 4 fenders missing.
A complete
Engine rebuild could cost as much as 800-1000 bux just rebuilding the top end will cost you 200-300 bux a Engine swap by time your done wont be much cheaper all the little stuff adds up quick.
The drive system is just like most snowmobiles and is just guarded not sealed like modern quads and side by sides that use a CVT drive system so you will want to avoid water and mud.
Climb up on the back of the ODY and jump up and down on the rear part of the frame see if them rear shocks do anything?
More detail pics would help others give you an idea on price and value.
Try using the brakes front and back see if they work you can spend days going through a brake system on a 350 getting it back into proper working order.
Sometimes a guy is better of to buy a running machine he can test drive but projects are fun also if you have the time.