(1) Can she do fix caps permanently? (2) After these caps, will the wudhu and ghusl be valid?
بسم الله الرحمن الرحيم
If after filling the tooth there is a need to get the cap fixed for future then your mother can have it and if the cap is fixed in the teeth permanently and it is not possible to remove it after much efforts then in such a case that cap shall take the place of a permanent tooth and thus your mother can have ghusl and wudhu in the same state.
Allah knows Best!
Darul Uloom Deoband