Changing Apple ID on iPhone - how is non-iTunes data affected?
Any purchases that she made with the previous account are the biggest problem as they are non-transferable. This would include music and movies, as well as apps. Since you mentioned that she only downloaded free apps, it shouldn't be a monetary problem. Because updates will require you to login to the old account, it would probably be better to re-download the apps with the new account. That way updates are seamless and easy.

iMessage (or SMS and MMS for that matter) shouldn't be a problem at all. All the old threads and messages should stay in tact and be usable like nothing ever changed. Call history isn't something that iCloud, or an Apple ID has anything to do with, so the change will also be without consequence there.

Yes, change Apple IDs, create a new backup and you're good to go. 

Side note: iPhone actually handles Apple ID changes very easily and smoothly. Some people have two Apple IDs in general - most by accident - and they will change back and forth for app/music/movies purchases.