Why mobile is unresponsive when battery percentage is above 60-70%?

Hi

I have a strange problem.

1. Charging light will be on even after i stop charging my mobile

2. When the mobile battery percentage is above 60% or 70%, and mobile screen is locked for more than 2-3 minutes, it goes dead(touch won't work or the force restart)

Both the issues are solved when i pull out the battery and insert it back, it works fine after that. So right now, I am always keeping the battery below 50%.

Phone has a broken screen but the issues happen only when the mobile is charging or battery shows above 60% or 70% percentage.

If the battery is below 60%, i don't see the second issue happening. Couldn't figure out what is causing this :(