Yes, home visits for new preschoolers is very common. In fact, I think it's a hallmark of a quality program and when I had my preschool, I always did a home visit. This gives the child a chance to feel like the teacher "knows" them-- they usually visit for about half an hour, meet the family members who are home, play a bit, get to see where the child eats and sleeps.
If you can, try to schedule the home visit for the weekend. This is really for your daughter's benefit.
As for the car seat buckle-in, I would ask the teacher directly about their philosophy in that regard. It may be that helping the kids into the car eliminated some of the 'negatives' that happen during the pick-up transition. Some schools have to deal with parents that linger, don't leave during pick-up, the pick-up meltdown, or parents who end up chatting with other parents while the kids are needing their attention.Many of the preschool teachers I know (myself included) have a 'get your kids and go' policy. Kids need to be the parent's primary focus at pickup, but from my experience, they often aren't. I wonder if it's to streamline things a bit, so you pull up, the caregiver loads the kid in, and you go. Both my preschool and my son's preschool had the parents and children meet outside. (I kept up a blog regarding preschool activities which I updated weekly, important info was sent home on a note that day; other schools do newsletters.) Just my take on it.
And to Debra: I'm really sorry you had such a bad experience with your teacher/home visit. What you described is really not the intent of most home visits. I've seen messy houses, I've seen beautiful houses... what I am most interested in seeing is how the child is in their own home, what they like to do, and what level of maturity the child is at for their age. This often helps me to make any accommodations/adjustments ahead of time and helps the transition to preschool to be more friendly because we've already connected. I wasn't there to judge, I was there to learn. I know my house was far less than perfect when my son's teacher visited-- neither of us cared. :)