If I pay the back taxes on a property do I own it free and clear?

No, first you can't just pay the back taxes, if you go to the court house and pay someone else's taxes you just pay the tax for them.

County court houses will have a auction normally once a year, ( some more often) at the sale you will get to bid on the property. It may sell for the tax amount or it may go for 1000's more than the tax amount, depend on how many people are biding.

This is where it gets hard, in many states, what you get at the sell is a tax certificate, it does not give you ownership, merely a tax lien of sorts, and the original owners have a redemption people from 1 to 2 years normally in which the original owners can pay you back your bid plus a percent interest, my last one was at 10 percent interest. ** still a good investment if you make 10 percent on your money.

In a few states you get a actual deed at the sale.

Most property that has a lien on it from a bank, the bank will pay the taxes and foreclose not lose it for taxes.