One problem with property taxes is that they do not capture the ability (or inability) of the property to generate income - basically, whether and to what extent it is capital.
We also do have taxes on income produced by capital - that's capital gains - but, as the article points out, we tax them significantly lower than regular sweat-of-the-brow income, and offer more loopholes. In effect, our economic system incentivizes rent-seeking over labor.
In most areas, yes. There is a property tax that is charged as a percentage of the land's value. If the owner fails to pay this fee to society, society revokes his ownership, forcefully seizes the land if necessary, and resells the property to another person who is willing to pay the imposed fee.