If you know that a house was abandoned, and you pay the back taxes on the house, do that make you the legal owner?

No, that only pays the other persons taxes for them.

The County will after a number of years of unpaid taxes offer the property for sale, This is normally done once a year at a tax sale. It will be done at auction. And even after paying or "buying" it at auction only a few states allow you ownership at that point, most require you to wait one to three years to allow the owner to redeem the property if they want to

I yield to Fr Chuck's greater wisdom on this issue.

BTW, this is really NOT a tax questioon, but rather one of real estate.