I Was Just Wondering How Long Do the Stitches Stay Strong and Hold Everything Solid in Place? (FUT Hair Transplant)

Only your surgeon knows what was done on your particular case. Unless there was someone standing to him/her.  You should ask your surgeon on the type of suture or when to expect the sutures to remain.There are many different types of sutures that dissolve at different time frames.  Only your doctor can tell you which one was used.

Sutures that are left in place take many weeks to dissolve. Don't worry about the sutures, they will dissolve in their own time

You will just have to give the donor area 6-12 months for healing to take place. Unless there is an open wound, it is unlikely you would need any immediate care. Your doctor would be the best judge of your situation.