You dont need any vaccination to travel to Turkey. Also there is not any mandotary vaccination.
yes
Yes, even children need passport to travel. Especially when it is international.
yes
No, you need a valid passport.
Yes of course you can, but you need to get a visa in Turkey first.
From where?
yes
yes
Children would need help getting travel documents and a driver's license. These are things for which children need adults' signatures.
Movement poss
Yes, they do.