Hi there! It sounds like you're dealing with two separate issues - rapid battery drain and display/touch problems. Here are some things to try:
For Battery Drain:
1. Check Battery Usage by App: Go to Settings > Battery to see which apps are consuming the most power. Facebook seems to be a big drain based on your screenshots - try limiting background activity or using Safari instead.
2. Turn Off Background App Refresh: Go to Settings > General > Background App Refresh and disable it for apps you don't need.
3. Reduce Screen Brightness: Lower your brightness or enable Auto-Brightness. The display is one of the biggest battery consumers.
4. Disable Location Services for Unnecessary Apps: Go to Settings > Privacy > Location Services and set apps to "While Using" or "Never".
5. Check Cellular Data Usage: Since you mentioned this happened on mobile data, go to Settings > Cellular and check which apps are using the most data.
6. Enable Low Power Mode: Temporarily enable this to see if it helps stabilize battery life.
For Display/Touch Issues:
1. Clean the Screen: Sometimes dirt or moisture can cause touch issues. Clean the screen with a microfiber cloth.
2. Restart Your iPhone: Hold volume up, volume down, then side button until you see the Apple logo.
3. Check for Display Damage: Since remote diagnostics found a display issue, this could be a hardware problem. Even if there's no visible crack, the digitizer could be damaged.
4. Update iOS: Make sure you're on the latest version - Apple often fixes touch-related bugs in updates.
5. Reset All Settings: Go to Settings > General > Transfer or Reset iPhone > Reset > Reset All Settings.
Since remote diagnostics already found a display issue, I would strongly recommend visiting an Apple Store or authorized service provider. If your phone is under warranty or AppleCare+, they should be able to replace the display for you.
Hope this helps!