Do you have to pay the property fee for a whole year if you live at home for half a month a year?

Yes, the calculation of property fees is not based on the length of your residence.

But whether you live or not.

If you don't live at all, you can apply for exemption from property fees in accordance with the policies of local government departments.

Or pay a part of the property fee, which is generally about 20% of the total cost.