The answers will vary depending on the voucher plan's specifics, but here's how the Texas proposal from back in the day would have worked.
I'll bite. How does school voucher work?
The parents of poor students in underperforming schools would have been given a voucher to send their children to the private school of their choice. Other programs are broader, but the Texas program was a pilot program designed to help a specific group of students. It isn't that Grusendorf wasn't for a broader program. He was, but he wanted to start off with a program that would be easiest to sell to the rest of the Legislature and to prioritize kids who needed it the most. Even though he was a pretty conservative lawmaker, there was a social justice element at play. He had special concern and sympathy for poor kids stuck in terrible schools, which is why it resonated with some black and Hispanic lawmakers who weren't whored out to the government school lobby.
The voucher did not consist of the entire school funding for that student. It left quite a bit of the funding with the public school (to account for fixed costs), which meant that the per-pupil funding for the public school actually increased.
You pick the school you want, anywhere that you can reasonably drive to each day?
Yes. And if the school was in the nearby area, public school buses would still provide transportation to that student.
The voucher makes it free?
Effectively, yes. The private school had to accept the voucher as full and final payment. Grusendorf didn't want the private schools to take the easy money and then gouge parents for whatever they could sucker out of them (like universities do with financial aid and student loans). That wouldn't have done anything for poor students.
What if the school is full?
Then the parent would have to find another school. Nobody was going to force private schools to expand their capacities.
Can the school kick out pain-in-the-*** students from out of district?
By "the school," I assume you mean the private school. If so, yes. They were permitted to have their own disciplinary systems, which could include suspension and expulsion for bad behavior.
It's important to understand the point of vouchers. It isn't to save every kid. If a kid is a ****-up and has crappy, checked-out parents, vouchers aren't going to save that kid. The point is to help kids who are on the margins - kids whose parents do care but who are stuck in atrocious public schools. It's to reward those parents for caring and give their kids a chance at a real education rather than waiting on the school districts to suddenly get a conscience.