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The mess/dust can be fairly easily contained to the room you're working on. Open the windows and stuff towels round the door etc. So I reckon you could do it a room at a time if you wanted to. I would do the hallway last if it were me as that will obviously see most traffic and can't easily be blocked off for sanding/finishing. Rent the machine for two days with the idea of doing one room. You might get it done in day, but at least you'll have the option of taking it slower and working out how best to use the machine. Then when you do the others, you'll have the experience to just get it for one day to do one room, or a weekend to do two.
Those boards look fine to me. The stain is already scratching off, so the 40 grit belt you start with will rip it off no problem. Be sure to go around knocking any nail heads down below the level that will be sanded to. The belts will chew through them no problem, but the sparks + wood dust are a bit terrifying when it happens and you are essentially creating sharpened metal blades if you just sand through them.
Sanding wooden floors. I know a number of people have done this recently with enviable results, so I was hoping to tap into that knowledge. I have a couple of questions - pics of my floor below.
Cheers!