Water damaged. Bluetooth & time problem.

I happened to drop my iPhone 5S into the hot tub. Let it sit in rice for 36 hrs. Tore phone apart, replaced battery, things are working again (using it to type this). Besides needing to replace the screen now (background lines & no longer auto-rotating), I'm having issues with:

-Bluetooth

-Date/Time

-Bluetooth just keeps searching and doesn't allow me to turn it off. Keep in mind the Wifi is working just fine.

-After I update the date/time, it only stays current when using phone. If I put it on lock and let it sit for an hour or a day, the time won't change. However, the notifications I receive from applications have the correct time on them. It's annoying. Read where I might need to replace SIM card, but I am getting great signal, all calls/texts on time, and LTE speeds.

I reset the network settings, hard rebooted, update to 8.3, and still no bueno. Any advice besides buying the iPhone 6, which I just might now haha, would be very appreciative of!