carseats - yes they will install it from scratch for you, but I attempted it first and they fixed it, lol.
Make sure you're allowed to use the LATCH hooks in the middle seat on your car... just because the hooks are there, doesn't mean its safe. Kind of hard to explain, but the hooks may be only for side installations (passenger side is 2nd safest position). The hooks for the center have to be connected behind the seat if its safe to use, mine were not, they were only connected to the hooks by the doors.
yes, they have everything you need for baby in the hospital.. just bring the carseat (keep it in the car until you're ready to leave, lol), an outfit for going home (my hospital won't let you dress them in your own clothes for security reasons until you're ready to leave), a blanket for bundling them in the carseat though I forgot that and the hospital gave me one of theirs which is pretty awesome flannel blanket, great for swaddling early on.
For yourself, bring a camera, your cell phone, charger, going-home clothes (you will still need maternity-wear) and toiletries. I had lots of other stuff packed and didn't use it at all though. My friend wishes she had brough her own pajamas.. but I was wearing the big mesh underpants with an ice pack and maternity pad shoved in there so I didn't want to wear my own clothes.
Take whatever you can from the hospital.. diapers, nose bulb (they really are way better than any you can buy!), bring that squirt bottle they give you, the witch hazel pads, any extra maternity pads if you're still bleeding heavy.. I took some extra mesh underwear too since I was dripping blood as I pulled my underwear down and sat on the toilet.. didn't watn to stain my own underwear. Heck I even took the pink bucket they gave me to wash my pump parts since they said they were just going to throw it out. I now use it on my kitchen counter to hold clean bottles and nipples, lol.
the Sitz bath thing was kind of useless at home.. it just fell in my toilet since my seat wasn't right for it I guess.