I (usually) start with "I hope you're doing well today" and move right into my questions. I've found that that method satisfies the judges who expect some sort of niceties, while not alienating the judges who think you shouldn't "waste your time" in that way.
Same. Personally, I think that asking "How are you doing?" is unnecessary; it not only takes more time than is needed but also seems like a purely insensitive formality as the questioner rarely is concerned about the actual answer.
This isn't to say that formalities don't have their place, of course; merely that "How are you doing?" is a personal question that, it seems to me, is somewhat out-of-place in a debate round. Simply stating "I hope you are doing well today; just a few questions for you" works well as an opener in preliminary rounds; I have never encountered a judge who had a problem with it. In outrounds, I will usually start by congratulating my opponent; though somewhat overdone at times I find it to be a respectful formality that is expected by most experienced judges in our region. Regardless, I think the main thing is to find an opener that is natural for you and yet exudes professionalism and respect to the competitor that you are cross-examining.