You have to get the screen replaced from BLU service center or you can buy new LCD screen online and get it fixed from mobile repair shops. However, I will suggest you to contact service center once and ask for the solution for broken LCD display.
Yeah, something might be draining the battery. Try these things. 1) Turn vibration off for notifications as vibrations need more power to get operated 2) Turn off Bluetooth, data and other connectives when not in use 3) Do not charge your phone overnight as it reduces battery life 4) Use cache clearing apps to clean up RAM and background Apps There are quite number of tips that you can follow. You can check this link which I found best https://www.pricekart.com/blog/tricks-to-save-battery-power-few-hours-more Suggestion: If your phone battery drains very frequently even after following above tips then it is the time to replace the battery with a new battery. Make sure the new battery is original and branded.