"Would I report mortgage interest paid by my ex wife?"
No. To deduct mortgage interest, you must be an owner of the property, and obligated on the mortgage, and be the person who actually paid the mortgage.
If you were required to pay the mortgage under a separation or divorce agreement, as a form of spousal maintenance or alimony, you might be able to deduct part of the interest as described here.
https://www.irs.gov/pub/irs-pdf/p504.pdf
