I'm using my mum's Apple ID on my new MacBook Pro, so, because of iCloud, I'm receiving all her emails, I have all her contacts, etc. I just want to use her Apple ID for iTunes, the AppStore and Facetime. Can I stop sharing all her data?
Go to the Apple logo in the top left corner > System Preferences > iCloud > Uncheck what you do not need or sign out all together if you want.
I recommend only checking off only what you do not need while keeping Find my Mac on. This way you can still track your MacBook Pro incase it goes missing.
On the other hand, if you choose to sign out from iCloud, your iTunes purchases, FaceTime, etc... will not be removed or affected.
Hope this helps.
Go to System Preferences / iCloud and, either Log Out or Deselect each of the iCould applications you don't want.