Can Mother remain landlord if not property owner?

[Jim Lin]

So we may be given a property from my mother (currently rented out 2 units) and wondering 3 questions:

1. if she can continue to lease out the property under her current lease agreements and collect rent (and keep it). 

2. In this situation, does the renter need an agreement with my name on it? 

3. and also if she keeps all the income, does she report the income or do I for taxes?

I dont know where to begin looking up this info! Thanks!