Yes, you can put polyurethane paint over eggshell in latex or eggshell in oil.
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Can you put stain in polyurethane to darken the color?
More important is, that both paints are of the same kind (like: oil-based paint, acrylic paint, latex paint). Semi-gloss is more easily painted over then high gloss, but first better find out what the old paint layer is made of. Check with the help of alcohol - if paint comes off in any way when you rub it with a cloth of alcohol, it's latex or acrylic paint (and can be painted over with acrylics).
Latex paint is an indoor paint, which will not work very well on siding; you can paint it on, but it is going to peel off pretty quickly. Use an enamel paint.
You should never paint a deck, the paint will peel (unless you live in a very arid climate I guess. The deck may be stained, you can put either oil or latex stain over old oil stain.
Yes