Sounds like your phone took quite a beating.
You probably need to order the Lightning port that includes the microphone as well.
My suggestions would be to follow, very carefully, the appropriate guides found here. The iPhone 5S is not a difficult phone to work on but like any iPhone, there are traps to avoid. Always disconnect the battery first, keep track of your screws as they are practically all of different lengths and if you put a long one where a short one goes, you could be in deep trouble (research Long-Screw Damage for the horror show). Everything is very delicate inside the phone so you shouldn't force anything at all. If something requires force, you are doing it wrong.