I would surround it in rice for a day or two. Maybe use a heat gun gently too it. You have to be careful, moisture turns to water, water has minerals in it which will destroy your phone. Keep us posted.
It might be that the filter got wet and all of the allegerns and dirt in the filter are now starting to release odor. I'd take the filter out and spray it out, let it dry and maybe buy a new one if its that bad. Keep us posted.
This is probably a software problem, first you should put your phone back together. Make sure it has some charge, then hold down your home button and power button in tell you see an apple appear. Then let go of your power button, you should see a iTunes screen pop up. Oh and also have your phone hooked up to iTunes this whole process, this will reset your phone. But should fix it. Keep us posted.
There is a way to get into separate screen on the boot up, there you will find drive settings and such, this happened to our Mac. And I watched a video on how to do it. If you just research it some more on how to get the the boot setup screen that should fix it. Keep us posted.
Well heat comes from something short circuiting, and right above the speaker is the battery. When you replaced the screen did you open the battery input cover? If you did there where rubber things on top of some of the inputs also on that board. If those where removed it could cause heat. Keep us posted.
The screws that hold the screen in place (on the bottom next to the charger port) may have broke off the bracket, or the bracket may have completely brokenoff the screen. Not much you can do, maybe open it up and see if that's the case, and invest in a new bracket (if they sell them) or a new screen. Is it in a case? Best of luck!