Chosen Solution

Do I need to replace the battery adhesive once removed, or I can reassambly the phone without the adhesive?

I would use some sort of adesive just to hold it in place so it doesn’t move about.. It doesn’t have to be as strong as apples concrete adesive lol normal 3mm will do

Restoring everything as original is the whole point of repairing anything. Just buy the adhesive with the battery.