"Apple logo then blue screen"に関する回答Is just the screws. I had the same problem. Just look at it: http://www.iphonebits.co.uk/iphone-5s-blue-screen-solution/ Everything you need is there.
"Microphone and home button does not work after battery replacement"に関する回答I have the same problem. Just after battery replacement. Microphone works on vídeos or calls using speakers, but doesn't work on recording notes. Home button doesn't work too, but Touch ID works perfectly.