M.S.
Cleavanessa, You're doing a great job!! We worry so much, don't we?
1-My son didn't even try to crawl until almost 9 months (he walked at 13 months). My daughter has been poised to crawl since 7 months and now 3 weeks later, I'm wondering if maybe she's going to skip crawling. She sits on her hands and knees, rocking, and screams. Just can't figure it out! I've done a lot of reading and I never read about there being a problem with kids who don't crawl. I wouldn't worry about it.
3-My daughter HATED her infant carrier carseat and when we upgraded her to a convertible she was much happier in the car. That said...I do have a friend whose child was like yours. She arched her back so it was impossible to put her in the car, and then she would scream the whole car ride. She's going to be 4 years old next week and she still is not happy in the car. From what I can see, she doesn't like being constrained, especially having the belt tight over her crotch. I think a little padding might help her there, but really she just doesn't like the carseat and there's nothing you can do about it but make her happier in other ways. Her mom doesn't run errands with her - one stop only, or she leaves her at home with Dad. But it did get much better.
4-Sleep is my big obsession. Sounds like your daughter might be overtired. When they are overtired, they sleep less and less and we as parents become more and more desperate (and I get a little crazed...). Babies her age need at least 14 hours of sleep a day. Are you putting her to bed early enough (sleep begets sleep)? Putting my almost 8-month old daughter to bed earlier and giving her a bottle right before bed (but putting her down awake afterward) solved our problem. She sleeps from 6pm - 6am or later, sometimes wakes around 4 but goes back to sleep. She also naps 1-1.5 hours in the morning, and 1-2.5 hours in the afternoon. You're in that transition stage of sometimes needing the 3rd nap but probably not often anymore. My son, however, slept great at night and took 30-40 minute naps during the day, until we transitioned him to one nap at 16 months, and now he takes great long afternoon naps. Don't give up! I really liked the book "Healthy Sleep Habits, Happy Child" to learn about sleep. I learned to separate MY issues from my kids' needs. I did cry it out with both my kids - the later you start it, the longer it takes to settle in. My son didn't sleep through the night until he was a year old. My daughter does it most of the time now (and I mean a 12 hour stretch without waking).
You're doing a great job. Continue taking it one day at a time and remember, you're doing the best you can!