The Safety Guide says that the Vita has a 2210 mAh built-in rechargeable Lithium-ion battery. I'm sure the Vita has a circuit to prevent overheating if overcharged, since most new electronics today have this feature. I use my Vita plugged into the adapter all the time, I hardly use it on battery when I'm home.
Battery life depends on brightness and I think internet connection.
If you like to download a lot and have PS PLUS, and play music, videos and games then 4gig memory card is too small.
If you like rpg I recommend: Persona 4 golden.
action/rpg: Gravity Rush
action adventure: Uncharted