Shingles is caused by the same virus as chickenpox, basically if you have had chickenpox a small amount of the virus remains asleep in your body, it can reactivate and this causes shingles. However you cannot catch shingles from a person with chickenpox
No CP won't give your mum shingles. By the way I believe there is a vaccination for the elderly against shingles now, I seem to remember seeing a poster at the GP surgery, might be worth your mum enquiring.
Had the same thing recently with my grandparents and yes, you can get cp from shingles (but shingles are less contagious than cp) but you can't get shingles from cp. once you've had cp, the virus stays in your body and can come back as shingles later in life, but it's more to do with being run down and your immune system being low. It's not because you've been in contact with cp. like a cold sore, it just flares up when you're run down.