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.
You remove oil based paint on tile floors by using a strong detergent mixed with water and a soft cloth
Scrub it with warm water and a sponge sander block.
What they call "oil base paint" is really called "alkyd base paint." So yes, you can do that.
Baby oil will remove oil and latex paint from skin. It will not remove paint from most rigid substrates though.
Don't mix them, your inviting trouble
Yes, you can. You can always paint over with same paint.
Scrape it with steel spatula, get residue with Goo Gone.
Take the door outside and use a chemical stripper.
Yes, you can.
Yes. Clean and degloss the oil based paint, apply an oil based primer, then apply the water based paint.
Yes, you can