You must use a lot of water, soap, and scrub hard.
Not directly. You will need to use a primer made to adhere to oil and will accept a latex topcoat.
Latex.
You have a contradiction ! - Latex primer CAN NOT BE oil based.
Either oil or latex primer can be used over interior latex paint.
Doubtful. You would definitely be better off using a good latex based primer.
It's primer made with a latex or acrylic base. You can use any kind of paint over this.
I would use Kilz latex primer.
You didn't mention whether you were using latex or oil based primer and paint, but generally the point of using primer is so that you can paint over it with any form of wall paint. Just read the label on your primer can to make sure it is compatible. On the other hand, if you wanted to paint the primer over the satin gloss, you need to sand the surface lightly to remove the sheen of the paint and provide a suitable surface for the primer to adhere properly.
paint it with a universal primer such as "BLOCKER" brand first Yes, you can. My preference is to use oil base primer under latex (water base) paint, because in my experience the oil base primer lasts longer. It stays stuck to the wood longer. I think latex primer is basically bogus. I have wasted a lot of time using latex primer and it comes loose and I have to sand it all off and use oil base primer. Latex primer does not work. Just like latex paint sticks poorly to bare wood. Latex paint does not have much "stick" (also called "tack"). It is a thin sheet of rubber, and there is very little "tack" to it to keep it glued to the wood. Latex peels off readily, once you put a knife under an edge.
Your ceiling may have been oil based, or really anything other than latex. If you used latex primer over oil then there is really nothing you can do except remove it and get a super low gloss oil base.
NO ! - woodstain does not use a primer.
It depends what kind of finish you will put on it, and whether it will be indoors our out: Indoors, latex paint: use latex wood primer Indoors, varnish: no primer required but can be stained, may need multiple coats Indoors, oil base: use an interior oil base primer Outdoors, latex paint: use an exterior latex wood primer Outdoors, varnish: no primer required but can be stained, use exterior varnish Outdoors, oil base: use an exterior oil base primer It depends what kind of finish you will put on it, and whether it will be indoors our out: Indoors, latex paint: use latex wood primer Indoors, varnish: no primer required but can be stained, may need multiple coats Indoors, oil base: use an interior oil base primer Outdoors, latex paint: use an exterior latex wood primer Outdoors, varnish: no primer required but can be stained, use exterior varnish Outdoors, oil base: use an exterior oil base primer