Hello Mirrum,
In America children are enrolled in kindergarten when they are five years old. You can enroll them at four if their birthday is on or before December 31st of that school year.
Traditionally kindergarten is a half-day, either morning (8 to 11 say) or afternoon (12 to 3). Some schools now have all-day kindergarten. Kindergarten is not preschool or first grade, it's in between. I believe a child must pass kindergarten to be accepted into first grade.
In first grade the children are expected to work at their desks, read, write, concentrate more. In kindergarten, I think they have a more relaxed atmosphere, there's toys and games and snacks. But there is learning too.
Preschool is completely optional, often used as daycare. There is learning involved, certainly it helps kids prepare for kindergarten. Personally I put my first two in preschool because I thought they needed some socialization, but my second two stayed home with me. I didn't see much difference in them when they reached kindergarten. I've never heard of a free preschool.
I can't help you with your visa question. I tried a google search but didn't find much. Perhaps you should search for the Board of Education in the area you're moving to, and contact them directly.

 

i'll answer your last question since the other reader answered the others. i don't think your fiancee visa will affect your son's enrollment. my mom is not a u.s. citizen. all she had was a green card and when i was at that age, if my mom had to pay because of her status she probably couldn't afford to put me in preschool and/or kindergarten because we didn't have any money at the time. the only time you'll have to worry about your status is when you're applying for a job.

 

This may be true in some areas, but definitely not all. I can say for sure that in North Carolina, Iowa, and Colorado a child can start first grade without any preschool or kindergarten.

 

I have 2 boys who have been in both the UK and USA school systems
To answer your question, first grade starts when the child is six, so they will have their seventh birthday whilst in 1st grade.
Kindergarten is the previous year,so they start this when they are 5, therefore having their 6th birthday during that year.It is more like our "nursery school" ie more play related although they start learning their numbers etc here. Usually Kindergarten is part of the public schooling system so you will not have to pay. However'like the UK there are private schools and church schools that have fees
Pre-K is the year before that. That and Pre-school you will have to pay for as it is in esscence day-care.
Kindergarten hours vary but usually 9 thru 3ish. They usually make the kids lay down and take a nap here.
Not sure about the visa question. I'm sure it won't be a problem since we are innundated with mexicans who don't have the paperwork. They are very hot on innocualtions so you may want to check with the school on what is required.