I don't want to hold my case all the time. Can I prop it up to watch videos or movies?

Many cases allow you to fold back the cover and operate or watch your iPad at a comfortable viewing level, usually 35-degree and 65-degree angles.

Can I still easily charge my iPad mini when it's inside a case?

This is possible in most cases. Each product varies, but iPad cases usually have precise cutouts for all the jacks, ports and buttons.

Is there any chance of my Retina screen getting scratched while it's inside the case?

It's impossible to say there's no chance, but many iPad cases come equipped with a soft suede interior that not only safeguards against scratches, it also helps to clean the screen.