The IRS and tax law should be looked at for all such questions.
The people who write the tax code are masters of combining collectivism with private property ownership.

Property ownership simply means that you have a "bundle or Rights" in regard to that property. They consist of possession, control, exclusion, enjoyment, and disposition.

The rights have nothing to do with any other contract you have entered into with a government (I promise to pay taxes as a citizen, if I do not the government can take any value I have stored in my home)

The rights have nothing to do with any other contract you have entered into with a lender (I've signed a promissory note with the bank and have used my home as collateral, if I don't pay the bank, they can take the bundle of rights that is ownership my home)

I'd also like to correct a statement you made.
In the U.S., the "collective"(government) cannot take your home. They can merely take the "equity" you have in your home. They cannot take your right to the house.

So, in a society that is becoming more and more collective every day, it may be a good idea to "own" property so you have the bundle of rights, but not to build equity so the collective has no recourse.

It depends on how you file your taxes.

If you claim that a portion of the house was used for business, then you get to deduct expenses to heat, power and maintain that portion of your home.
However!!! When you sell (trade) your home, that part that you have claimed as business must be returned to the collective, since you have personally already gained (did not have to pay property taxes on that portion on the home), and if you have any gain from the sale of the property you need to return that gain to the collective, in the form of a check (or gold) sent to the government (leaders, counsel, parliament, elders, whatever).

This is a simple case of accounting and applies in any society that has trade.

If it suits the government interest (especially for tax revenue), they will invade our privacy.

Anarchy has a pejorative connotation for an interest. This is nonsense.

Anything part of or attached to the commons is subject to the will of the people, (our government)

In all honesty I can't imagine an anarcho communist society existing with out an anarcho capitalist / voluntaryist society already in place. I say this because ancaps/voluntaryist would adhere to the non aggression principle and allow people to buy up as much property they wanted so that they can create the society they wish to have on their land. If said people wish to live in said situation, that is obviously their choice.

It is private property owned by the owner. Employees are the equivalent of renters staying in a home they don't own.

Nobody knows the answer... which highlights the problem! ha