That's normal.

Newborns use nursing for a lot of different reasons... food, thirst, comfort, and even to help organize their thoughts and the world around them. It's like the one "known" factor in the world to them. Newborns can certainly nurse for long periods at a time - it doesn't mean they're over-eating, sometimes they get very little but they just want the comfort of sucking.
As for sleep, do whatever feels most comfortable for you and her. There's no right or wrong ways.

I always nursed Kate laying down at night so I could doze off... but then she would never let me put her in her own bed either, lol.
Good luck on nursing in public! It can seem like quite a production when you have a tiny one but it gets a lot easier as they get older and you both get quicker and getting it all set up.