My daughter is a disabled adult and receives SSI payments every month. Since she lives with us, she pays us rent every month. Do I need to report that as rental income?

You are not in the business of renting. You are just cost sharing. Nothing has to be reported. 

It depends.

If the rent you receive is at a normal rate (as paid for similar accomodation between unrelated parties), then yes, you should report as rent and deduct any rental expenses.

If you rent to your daughter below fair market value, the IRS considers that you do not rent your property to make a profit. In this case, you can deduct your rental expenses only up to the amount of your rental income. You cannot deduct a loss or carry forward to the next year any rental expenses that are more than your rental income for the year.

Mortgage interest and property taxes paid can be claimed in Schedule A as for your residence.

Please refer to this IRS document, especially the section on Not Rented for Profit on page 16 of this IRS publication on how to report income and expenses.