You remove oil based paint on tile floors by using a strong detergent mixed with water and a soft cloth
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It depends on the base of the paint. If it's an ordinary house paint, you should be able to peel it off.
If I was going to repaint this, then I'd remove both the latex and the old oil base with a chemical stripper. Then re-prime it and paint.
Scrub it with warm water and a sponge sander block.
Ceramic tiles are normally laid on a cement base. If the floor has any flexibility at all, the tiles will wind up cracking. But if you do have to install tiles on top of wood, then yes, the wood has to be sealed because the grout is mixed with water, which can damage unsealed wood.
You can try using denatured alcohol if it was latex paint. But it is probably cheaper and easier to just replace the vinyl cove base.
Scrape it with steel spatula, get residue with Goo Gone.
Take the door outside and use a chemical stripper.
Yes, but I wouldn't recommend it. You will regret it later. Tile needs a cement base to adhere to. A wooden base is not good for ceramic tiles. I have seen tile floors where people have tiled over the wood. The tiles are loose, cracked and unlevel. The grout is coming out and water seeps through the floor.
It depends on the condition, material and surface of the laminate. A linolium floor, for example, is soft composition with a textured surface. This makes a horrible foundation for ceramic tile, giving room to crack the grout between tiles. A hardwood-type laminate is smoother and harder which is a better foundation. That said, the best thing to do is rip the laminate out and start fresh.
Yes, you can.
Absolutely not and you should use the same manufacturer of the paint you have on there also. Sorry you can only use a chlorinated rubber base paint on a rubber base paint. If you try to paint with the chlorinated rubber base on top of a synthetic rubber base paint it will probably peel like a bad sunburn.