My sister lives with my mother. When my ma passes, is my sister allowed to stay there? Or worse yet, have ownership of the house?

As executor your duty will be to gather the assets, pay the bills and distribute what is left according to the Will.  If your mother wants your sister to have the house, she should gift it to her in a Will or in a deed which transfers title on death.  If not, you may be obliged to bring an action in small claims/justice of the peace court to evict your sister.