If my name is on the deed for a home, but not on the mortgage, am I considered a home owner?

Yes, you are a homeowner if on the deed. 

Yes, you are the owner. However, you can't deduct mortgage interest if you are not on the mortgage.

are you paying the mortgage?    if so, there is a concept in the law that allows an equitable owner to deduct mortgage interest even if not on the mortgage.  you would be required to take total care of the property and meet certain other requirements.