Yes.

Perfect. I prefer the first sentence because it is so direct and contains no subordinate phrases. You could replace "constant" with a better word. "Constant" is a good word, but it doesn't express annoyance, so you can find something better, like: "ceaseless" "endless" "nonstop" Those words describe something that cannot be avoided, and are thus annoying. "Constant" is a neutral word. Things that are constant need not be annoying: "the beautiful weather was constant today". You probably would not say "the beautiful weather was endless today".

Yes, both sentences are correct and natural, though they express the same idea slightly differently: 1. Your constant laughing annoys me. * This focuses on the action itself ("constant laughing") as the subject. 2. It annoys me that you laugh all the time. * This emphasizes the speaker's reaction to the habit ("you laugh all the time"). Both are perfectly fine and can be used interchangeably!

These are both correct!