"Aaron is a genius boy"

Both are technically correct, but the idiomatic usage is "boy genius".

"Genius Boy" sounds sarcastic to me: "Everything was going great until Genius Boy here turned out the lights."

I would say that the word "genius" in this context is being used as an adjective, which it is not - the adjective form is "ingenious". "Boy genius" is idiomatically preferable, as indicated elsewhere.

You can say genius boy in the same way you say, for example, ninja boy (ninja is a noun that modifies a noun); the correct expression you are asking for is boy genius, though.

Yes, you mean "boy genius" unless you are trying to create your own term.

I've never heard "genius boy", and "boy genius" is a standard term for "whiz kid": http://en.wikipedia.org/wiki/Boy_genius