You can change - yes. Just delete icloud account that you see in settings and when it asks you if you want to keep or delete information on the phone make sure you keep. Then sign in with another apple id.
Downside is that phones with different id's will not sync contacts or calendars, but it is not necessary in whole family.
I am not entirely sure you contacts disappear, cause of that, but that would be a start to find out if you are correct.
Thank you. I'll give that a try. If I press 'delete account' will it only delete the account on the device I'm using at the time (i pad) or will it totally delete the account and affect the other devices too? My son will never forgive me if his music, pictures etc disappear from his devices if I delete the account on my devices as, like I said earlier, we have six devices sharing the same apple account/ apple id. Hope that makes sense!
As long as you will keep the data when prompted, nothing will get lost. Photostream is going to get reset, but it would happen anyway past 30 days and it does not make you lose any pictures, they are still in camera roll. If you worried - start with one device, give it few days to make sure that everything is ok. Try to pick device that will not affect much. Once you verify that everything is fine go to next one.
If you only do that with icloud it will not affect music at all.