Your property tax rate can be determined by looking at the tax bill or going on line to the county assessors site and looking it up there, generally there is a basic rate and then additional bonds or fees depending on the property location. The value of the property was determined by the original purchase price and then increases annually as allowed by law. If you have inherited the property, check with your tax advisor or attorney to see how the value will be determined.
The income tax rate on a rental property is going to depend on your financial circumstances, consult your tax advisor.
By free and clear, I am assuming you have no mortgage on the property. That information is relevant for considering income tax advantages to owning real property, not in terms of taxes directly paid on the property. On income taxes, they have recently removed the passive loss deduction of up to $25,000 allowed each year...if you make more than $125K in income. So as of 2009, if you had expenses you could write off, like interest paid on a mortgage or taxes over and above what was received in rental income, as well as depreciation, those deductions may no longer be valid. Speak with your tax professional on your personal situation to see how that applies to you.
Right, whether you have a loan or not, you still have to pay property taxes for services provided by the State
Generally, in California it is 1.25% of the Purchase Price .
As your profile has you as a "Home Buyer" I will assume you are trying to determine what your annual property tax will be for a home purchase. Your question is exactly why I wrote the following blog post to explain how the TOTAL tax bill is calculated: http://www.trulia.com/blog/steve_ornellas_mba_re_mastersgri/
Property taxes are based on 1% of the purchase price. There a few other items that can increase the bill as well.