No, they will not mix,
No you can not.
Yes, you can.
You can always paint latex ( water based )over an oil based paint as the latex just dries on the surface. However don't paint an oil based over a latex paint. Oil based paints need to absorb into the wood or other surfaces or it will just dry and flake off. For more information on the differences and when or not to use a latex or oil paint please see the following article. . http://www.ehow.com/how_4713170_between-latex-oil-base-paint.html
Just paint it on if the latex is adhering well.
No, you either need to really rough up the oil paint with fine sand paper, or put a base coat on before you paint with your Latex paint. If you don't your Latex paint won't adhere.
no
yes. However, you cannot use an oil base paint over a latex primer. If you change your mind on the paint, you must strip the paint before you use an oil based paint on the primer.
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.
No, and in fact they won't mix.
Yes it can.
Don't mix them, your inviting trouble
If they are both of the same base you can. Satin paint can be an acrylic or a latex,or an oil. Check on the can cleaning instructions for base. Jason Pollock used both in his work 'Bluepoles' which hangs in the Canberra museum I think