Depending on what tools you have, I can think of two options. You could replace just the backlight on the screen (backlight is about $10), which would require you to solder a basic flex cable. The water is trapped between the layers on the backlight. Drying it will just leave a permanent mark (if not dried already). Depending on your skill level, I'd say it's a bit tricky to do perfectly. You need to be super careful to peeling off just the backlight panel and none of the lcd part. Also be careful not to crack the lcd. The more expensive option would be to replace the whole screen. Apple charges 129, but not sure if they'll do it for a water damaged phone.

I've seen this problem before and replacing just the backlight fixed it for me. It does require a little soldering to do though. Otherwise replacing the whole screen will fix it too, but will be more $$. If you still have warranty on the phone, take it to the apple store and get it replaced free.

You need to be using the original home button from the phone in order for it to work. The fingerprint sensor is uniquely tied to each 5s. Open it up and see if the clip came loose. Try cleaning it out too, there might be some dust/dirt in the way.

Does the phone get into the main menu at least? Can you boot into safe mode? Hold the power button until the power options appear, then hold the "power off" icon for a few seconds until a reboot into safe mode option appears. Did you ever connect a google account to the phone?

Try doing a network reset in the settings first. The only cell antenna you could have touched would be right below the battery connector. You shouldn't have need to pop that antenna out though. Anyways, check that and see if it's seated in. It has a single gold/brass colored connector with a somewhat thin wire running down it. Did you disconnect the battery before removing the screen? Also, was your phone bent?

Well technically yes, it does void the warranty.. You'll need to be super slick about it. You need to leave no trace of you opening it. So no fingerprints or smudges anywhere inside (so wear like gloves haha). Also, no signs of damage on the screws. And just to be ocd, put each screw back in where they came out of. If you do need to take it Apple for warranty purposes, you need to put back the original ssd. Make sure you get the right size ssd too.

Was it getting really good battery life the moment Apple replaced it? Not sure about that app, but cycle counts should be for each individual battery and not the lifetime of the phone. Put that battery Apple installed back in and take it to Apple and have them check the cycle counts. If it really is 1258 cycles, that's literally impossible if you bought it back in Oct of 2015 (if it really is a new battery). Some other explanation I can think of is that you're using some really cheap charger or the conditions in your area is terrible for the phone, like super cold or super hot.

Well does it still turn on? Have you opened the phone up and check what's corroded inside? What type of water got into it (drinking, tap, salt, etc.)? I'm guessing you don't have tools/equipment to handle water damage. So in my opinion, if it was really "bad" water damage, I'd just take it to Apple and pay them 329+tax for an out of warranty replacement. Unless you have APple care which will be a lot cheaper. Also, don't let a 3rd party repair place open it and leave fingerprints or any sign of being opened because Apple will then tell you to buy a whole new phone full price :P

Was the screen replaced before or something? Cracked? If you can open the phone up, maybe check if the connector came loose. If it needs a new screen, you'll have to replace the entire screen, not just the "touch pad."

Most likely it's either the battery or the u2 chip on the phone. You want a brand new genuine quality battery first. Difficult thing is finding them because even though they say "OEM," they're not.. Cheap batteries may have cheap battery cells and cheap components that may damage the phone, just like cheap chargers. I'd try doing a full clean reset on the phone first, charge it up to 100 (and leave plugged in for like an hour or so), unplug it, and play a youtube video or something and see how long it lasts. You should be able to get a few hours of video playback with full brightness. You could also try making an appointment to the apple store and tell them to check the battery health. They'll be able to tell you if it's good or not. Don't tell them you replaced it yourself though ;)