I have found the solution to the problem it seems.
For the problems with iCloud calendar invites not going through to calendar on iPhone, iPad, iTouch and so on or going to email instead.
Solution was found while I tried to sort out a problem with my iMessager, it kept saying could not validate as it was already in use. I also had the same issue with FaceTime on my iPhone after logging out, I couldn't log back on.
- Head over to appleid.apple.com
- Login
- Remove any old email email addresses that have been assiociated with the account (if there has been any) - this should sort it the iMessage and FaceTime issue.
- Change your password, making sure that it conforms to the new constrates set by apple (two letters, one upper case & one lowercase, one number and so on.
- Click "Save Changes"
- update all your login settings with the new password and it should work.
I have fixed my me.com and my fiancé me.com account with these steps. Hope it works for you all as well