Picked up TLOU. I've played through a bit - I'm in the school with Bill.
It's about as i'd expected so far - having played Uncharted games in the past. It kinda feels like a mashup of those and The Walking Dead [game].
I find the guns to be a bit awkward and clumsy but that is probably more to do with the controller in general. The melee combat is fine and I usually rely heavily on that when not sneaking.
Re: Bill - Yeah Ellie was a jerk to him but I find her to be a jerk in general. Maybe she is meant to just be a product of her environment - a child without proper discipline or role models.
As for the theft, I don't think things like posession would carry the same weight in a world like that - you'd get used to taking what you need and hoarding what you can use.
She took his things even after he [Bill] told her not to but she probably just wouldn't see anything wrong with what she did. Joel goes through houses raiding whatever he feels like.