Does memorizing have benefits on the brain ?

Yes: It develops discipline of the brain and learning. That said, there is no evidence that it prevents dementia or any brain disease.

Absolutely; Exercise: As embodied Soul↔Mind↔Brain↔Body creatures, the more we practice using what we have, the better we can perform at most things. Does using muscles trigger building more muscle? Does practicing doing anything (brain function/control in all processes is crucial) increase ability to do it better & easier down the road? Whatever we don't use does not develop as much & becomes weaker over time.