hi, you won't believe it but I live 5 kilometres from the airport!
1)house: you will find a 4 bed house for apprx 1000-1300 €
2)the airport is 10 km from rome
3)ciampino is very beautiful city
4)you can find an house in Frascati which is connected to ciampino via train (10 mins) and is more nice for kids.
5)schools:there are plenty of nice schools...there is one with only english lessons VERY NICE
if you have other questions ask!