iCloud Issues - Can't Log in at this Time

I have significant issues with my wife's account on new iMac using iCloud

In attempting to use apple id to login to iMessage and FaceTime I changed the relevant apple id password.

The iCloud interface wouldn't accept new password on mac although icloud.com worked just fine.

When I try to login to iClould - get a message Can't log in at this time.

When I try to sign out and remove iCloud (to try to setup cleanly) I do it (iCloud and Mail). When I log back in their still there in a disabled state.

Just can't work out how to resolve.

I am a new user to Mac, being using PCs for a long time, and I just can't work out what's wrong and how to get iCloud setup (mainly for calendars / docs) on my wife's iMac user account, and get iMessage and FaceTime to work.

If anyone can advise how to resolve I would greatly appreciate it.