It depends on several things... Is the pot still absorbent? A terracotta pot will suck the liquid out of paint, almost instantly drying it (makes it difficult to keep any liquid in the brush). You can seal it with any type of paint or varnish that won't be harmed by whatever you put in the pot (think water damage).
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If it has been fired already, then probably not. Are you using ordinary acrylic paint? It should go on just fine, I don't think it will soak in or anything. Do a test somewhere that won't be seen.
Probably not. Are you going to be firing it after you paint it?