1. Mum was cook, chauffeur, nurse, and entertainer all rolled into one. YES Mum was a woman of many TALENTS (or Mum had many skills): cook, chauffeur, nurse, and entertainer. Mum was multi-TALENTED/MULTIFACETED: cook, chauffeur, nurse, and entertainer It sounds awkward to say "mum was a woman of many parts". The idea being that with 'parts', you can change them out. Can't 'change' 'parts of a human, so we need another word here: talents, skills, multi-talented, multi-faceted.

The "multifunctional" sentence does not work because it makes Mum sound like a machine or other device. Remember to pay attention to the nuances of each expression.

Thanks Reed, I just added another one~

Yes, both of these sound good in English.