I'm not sure about the touchscreen issues (is it an original screen or e third party replacement? Third party could be an issue)
If you need to force restart the phone you can try this If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support at least then you don't need to wait for the battery to drain.
In order to try to stabilise your device, might suggest backing up your phone (if backing up to iTunes - ensure that you encrypt the backup - it is more complete that way), Turn off find my iphone if you have it enabled, then entirely wipe the phone using 'Erase All content and settings'. Then restore your phone from the backup. You'll need to reenter a couple of things (Apple pay or instance), but your phone will be pretty much set up as it before (but hopefully more stable)