Retirement tax questions

#1 - It is not income.   It could be considered to be a gift or just sharing expenses, but either way it is not reportable or taxable income.

#2 - What you describe is not rent unless you have a formal rental or lease agreement which would be very unlikely in a family situation like yours and the rental is intended to be profitable (and if your mother moved out, then you would rent to someone else.)

#3 - Not a tax question.  You would need to ask that to the agency involved.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**