This is Texas which has no income tax, so they have high property tax. It's about 1% per annum based on the appraised value of the property. Plus if it's a newer neighborhood, you pay an extra amount for the cost of infrastructure until it's paid off, usually called a MUD (municipal utility district) tax. Mine is an extra 1.2% so I'm paying roughly $1200/month in property taxes for my residence.

The property tax is based on the assessed value of the property. (Which can change over time, even if you bought it years ago.) And the tax ranges from 0.28% in Hawaii up to 2.49% in New Jersey. Most states are around 1%. There may also be local taxes from a county or city, which is typically a small fraction of the above.

Depends on where you live. Here in Washington state we don't have an income tax, so our property taxes are one of the few ways the government has to collect taxes. For that reason our property taxes are much higher than states that have multiple ways to collect.