On the topic of "there should be different varieties of helms", Space Wolves are well known for their Wolf Helm. That should definitely be an unlock of sorts.
Maybe have the no helmet option only occur after you reach a "rank" or "achievement". Maybe able to do whatever when you are on your ship, but not in a combat situation. Lore-wise, I think most marines would definitely keep the helmets on in combat.
Most yes(I certainly will), but there are a sizable chunk in fluff that don't. It should be an option from the get go, but whereas with a helmet on you shouldn't be able to be one-shot by a shot to the head by a bolt(unless it's in the eye) or a lasgun shot, you will be able to one-shot by a headshot from those without a helmet.