Yes, it's fine to charge your laptop to 100%. About once a month, allow your battery to run down to about 20%, then charge it back up to 100%. This allows the chemicals inside the battery to get mixed up, which will extend the life of your battery.
It is not likely that your laptop is not turning on because of the screen. It is suggested that you take your laptop to the nearby repair center and explain...
Sounds like either your battery isn't charged, is dead, or not inside your laptop. For Windows: when your laptop is on, you'll see a battery icon in the tray. It'll...