I am investigating a somewhat obscure area of number theory. Can I post a proposition and a complete proof and ask people to check it?
You are free to post such questions, but personally I am disinclined to answer questions of this type and I don't think I'm the only one. The problem is that complete proofs are long and annoying to check. If you know the subject well enough, you should be able to check it yourself. If you don't, say because you're not comfortable with concept X, you should ask about concept X, especially as it relates to some step in the proof you're not sure about. In other words, isolate the parts of the proof you're having trouble checking and ask yourself why you're having trouble checking them.