Chosen Solution

I replaced the iPhone 5s battery following step-by -step guide from ifixit. I have two problems:

  1. the screen is a little bit mobile and not completely fixed to the base/assembly.
  2. A new bluish area ( size of thumb print) is on the screen ( when phone in use) just above the home button. phone is otherwise working fine. I am letting the battery drain below 10% before charging it fully. so not sure on the battery yet. what should i do to fix the problems?

For the first part, it could be that your frame is bent, or that the part just isn’t fitting in there properly. You need to decide if you want to exchange it for a new part. The blue thing is damage to the LCD. Believe it or not it often goes away, after some amount of time. Since you have these two problems, it’s possible you’ll want to exchange the display assembly for the one you got, but you may also decide your phone is finally back to working, so you may not