A.
I would encourage you to talk to the school district's admissions staff in a month or two (as they're super busy right now) because they can answer most of your questions. If you're in ECFE (which you should be!!) you can ask about this in class and I'm sure you'll find parents who have used it. :)
I did not use the 4 year old program (let's call it 4YOP) because I am very satisfied with our preschool experience and I also prefer a part-time program. The 4YOP is basically a publicly funded pre-school program that is half day, five days a week. In the Montessori schools it is integral to the rest of their program but in other schools it's just preschool. There is no cost for the program itself. It can be difficult to get in, and preference for admission is given to those with low incomes or who meet other criteria (minority status or who need extra preparation to be ready for kindergarten, I think - this is where the admissions staff would be helpful.)
There's not really an advantage over private pre-school except that it doesn't cost you anything more than you already pay in taxes. It's also helpful for people who have an older child already in that school - the younger one can go to school at the same place and and same time and get child care for the other half of the day at the same location.