1) The distinction is most certainly not pointless, as I rarely deal in absolutes in terms of political economy.

2) Yes, after it's paid off and the mortgage lender has no claim on the deed anymore, then you can properly claim that the building is yours.

Of course, this still doesn't touch on the core issue that the land value increment (asopposed to the actual real estate,ie. The building) happens with no necessary labor input from the owner or resident, and which is shown time and time again to be the core of material inequality in society.