One of the hardest repairs i have done by far
sounds like you may have damaged the battery in some way, try replacing the battery!
Nope! there is no adhesive the screen just clips in!
The 4th gen doesn’t have a digitizer so yes you can just order a replacement screen and install it but you will need adhesive for it because it doesnt clip in like the 2nd gen
Sorry that this is literally 10 years late but, you probably damaged the ribbon cables during the opening process, you will need to order a new power button and a new display, these days it is literally impossible to find those parts so finding a new 2g on ebay is your best bet.