Welcome! I would hardly say you're a mess! Why are the new pedals stressing you out? Are they harder to clip out of? Or is it just that they're one sided?

A) Maybe you don't need to unclip both feet at the same time, every time - but you should be comfortable unclipping either. I have a hunch that you're doing this because you're not 100% confident that you can make the bike lean to one side or the other. Perhaps practice (with both feet unclipped) so that you can reliably go one way or the other. Maybe in a grassy area? That would also allow you to leave one foot in since they may be a bit harder to get started with if both feet are unclipped.

B) See A. Most people *do* have a dominant leg - but that doesn't mean it's a good thing. Being able to start/stop with either foot is a great skill to have - particularly when you realize the road isn't sloping the direction you need....

C) I don't usually come off the saddle either. I know it's not good form, but it's what works for me. I do tend to lean to one side, though - instead of trying to balance on tip toes. Perhaps try the drills in A and put just one foot down?

D) I often commute in regular clothes and don't usually feel comfortable with this either most of the time. I work on it, but it's not a natural motion for me. FWIW my DH rides with the faster guys and he doesn't do this either. No one has said anything to him.

E) This one is harder. I think bike handling classes like those offered by LAB might help you. They work with you on handling tight turns, what to do in different traffic situations, etc. I wonder if the handling would improve your confidence? I expect most of us have fallen over at one time or another. It's usually not that bad.

Good luck, and give yourself some credit! Sounds like you are off to a great start!