I agree that a carrier is a great way to deal with a baby that wants to be held all the time. I got mine for around $10 at Target.
Some babies just need closeness, especially at night. Neither of mine were sleeping through the night at 7 months...to me, it seems odd to expect them to. If your other three did, count yourself lucky!
If you can't get your little one to sleep on her own, I'd suggest co-sleeping. That way, when baby wakes up, 9 times out of 10, she'll see that you're right there, cuddle up, and go back to sleep. If she's actually hungry or dirty, you can change her or feed her quickly and easily, without having to get up. Everyone will get more sleep. :)
As to hitting and biting: I highly recommend that you don't hit/bite your child in order to prove that hitting/biting is wrong. As one mom here has said, you should lead by example. As another has said, your child is simply at an age where he has a hard time expressing emotions in an appropriate manner. With my son, we would put him in Time Out immediately if he did something like that. Then, when Time Out was over and he was calm, we'd tell him, "You were angry because _____________. You can't _______________ when you're angry, but you *can* ___________." My son is now three, and he doesn't hit or bite. He's very sweet with his little sister, and plays well with older kids, too. I think our method worked great!
My son tried getting out of his car seat for a while. He could undo the top straps, but had a harder time with the bottom button. I fixed this by using large, locking safety pins (you can get them online at cloth diapering sites) as a back-up for keeping his straps in place. Then, not only would he get in trouble for undoing his straps, but they wouldn't actually come off, either. After about a month, we took the pins off and had no more trouble.
Good luck! Sounds like your kids are pretty normal and healthy!