Sounds like the batterys "memory" has some defect.. You might be better off investing in a new battery if thats doing your heading.

Sounds like you have damaged both LCD and digitizer... Cheaper option would be just to buy LCD display and digitizer of eBay... Although changing the digitizer might be tricky if you are doing it for the first time therefore you might be better off buying the whole thing as person above suggested :)

erm depends how deep the part got stuck... You could try using the small screwdriver with magnetic tip to try to take it out by simply inserting it in the headphone port and slowly pulling it out without forcing anything... eventually you could try to pull it out with tweezers?

Hey up, open it up again and see if you haven't damaged the mobo as by looks of it thats the case. Also try to do a 'master reset' by seperating the mobo from the battery... simply take the motherboard out for 1-2 minutes. When putting it back together make sure you gonna connect everything correctly. I have had similar problem 3 or 4 times and doing 'master reset' helped everytime apart from a single time when i managed to break components off :(