1. Go over the entire floor with a rag damp with turpintine, use good firm pressure (elbow grease) this will clean any wax or other residue off the floor. 2. Get a dull 1" chisel, bevel side down, scrape off the paint splatter, you shouldn't leave any scratches since the chisel is dull (old trick from Grandpa) 3. Your floors if original, probably are not stained, any color is from the polyurethane aging and ambering. and it is almost certainly oil based. if they happen to be stained, matching is not that hard, it just takes practice. 4. The linoleum will most certainly have asbestos in the glue and the tile, I don't recommend DIY's touch it,(**) but if you do remove it wear a respirator and ventilate with an out blowing fan, if you can keep the floor moist, NOT WET, and remove the tiles with a scraper, be very careful not to go to fast or use too much pressure, you don't want to gouge the wood. ** My recommendation though would be to encapsulate the floor with a Ceramic tile. 5. After you remove all the tiles, sheets etc., you will have a glue residue on the floor, use a adhesive remver, to get this off, it's like a stripper, let it do it's work, don't rush it. It might take two or three times to get it. 6. After all this you will be left with the original floor, most likely, if you are gentle, you will still have a layer of poly, if you do you will be able to screen and recoat, if it's in bad shape, you will need to refinish the entire floor. There are orbital floor sanders, that take a little longer and use more paper, but they will not pit like a drum sander will, Lowes has them. 7. This is alot of work, and it is hard to give advice when I can't eyeball the floor, so I hope you have good luck and just take your time.