So its pretty clear that if a unit initiates a close combat attack, its target can only make an attack reaction (if any), which can only use other CC weapons. What about the other way around? Can CC weapons be used to react to a regular weapon, as long as the range is good?

Thinking in particular about what happens if you CC attack something but don't finish it, and next turn it attacks your CC guys. I'm not seeing anything that says they can't react this way, but I just want to make sure.

no rule at the moment that states you cannot react with CC weapons. the weapon you choose to react with must be withing range. so if you choose to react with the 3" then your fine but he could move back a few inches and attack anyways out of your unit's reach

Sure, but if they're moving away and you can still react, you can just react to the start of the move…on most units, anyway. Need to start playing with more melee…