Yes, the minimum age gap is usually 2 years, however many people would suggest that 3 years is a better minimum age gap. It does depend on the agency, there are a couple who prefer 3 years but it's 2 with most of them.
The average age of a child at placement is almost certainly 2 years old (at adoption finalisation the average age is now 3 years 5 months, and since it takes months to reach the court stage, that leaves you with children aged 2 on placement). The vast majority of adoptions are of children in the 1-4 age bracket, though there were a few hundred babies under 1 placed last year as well.
So I wouldn't assume older child. It is up to you which age range you ask for, and 0-2 or 0-3 is a common thing to ask for. As long as you're realistic and recognise that it may take you a longer time to find a child in that age range, there's nothing wrong with choosing that age range. If you do want an older child 4+, obviously you would have to wait a lot longer before beginning the process, but to be honest no one has any idea what exactly the adoption process and demographics of waiting children will be in ~7 years time!
With regard to schools, that isn't something the court would get involved in. When your child is ready to start school, it's the parents who choose the school, based on what the child needs. If your child isn't yet legally adopted but you run into problems with getting into school, your SW can given advice and other help if she/he can. So it's up to you.
Schooling will be explored a bit in the homestudy assessment. What they're looking for is a flexible attitude to school, an acceptance that your child may or may not be academic and it's okay either way, and they want to know that you'll choose the right school based on your childs needs. An independent school which fits your new child is fine.
If you go in to the assessment saying 'my adopted child will go to x school, for absolute definite', they might be concerned though (assuming you have a choice over schools). If your childrens independent school is a really academic school, they might also be concerned though, and they would want to see that you accept your new child might not be academic enough, and you would just as happy with a different school that was better for them.
So in the adoption assessment basically it's not so much about individual schools, as your own attitude to schools and educating your children
Hope that helps!