1) property which has remained undivided for four generations would be ancestral property
2) in your case property has been divided among family members . deed of settlement has been entered into
3) your mother got her share in property on her mother demise
4) mother can bequeath property to whom soever she pleases
5) your mother can sell property without her children signature
6) mother can execute gift deed for her property
7) other children can challenge gift deed but they have to prove it was executed under coercion or undue influence