Hi
Yes it is possible to solder your webcam cable back together but it’s not going to be easy as it will require complex micro soldering
What I would do here is buy another faulty display and strip the cable back so you can see which cables go where as I doubt you will find a wiring diagram
As for the stripped screws there’s not much we can do without it going to the extreme ,you could use superglue and glue the screws back in or you could use red loctite BUT BE WARNED it will never ever come out again easily if you use these methods but it will hopefully fix the issue
Hopefully this helps
If you need any more help please ask
Thanks:-)