My mom is 50 and has had dementia for months now. Is this age when it normally sets in?

Not exactly. Early onset dementia is quite rare, and often occurs in clusters with a family history; i would ensure that there are no other reversible contributants to her condition...
Not usually. Your mom is suffering from early-onset dementia, which is defined as onset before age 60. In those cases, it is very important to be sure she has a very complete workup, including testing of the fluid that covers the brain, for other causes. A minority of cases of dementia can occur at the age of 50, and there have even been cases as young as in the 20's or 30's.