Warhammer 40K Tabletop VII: Common Sense is not RAW.

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I can't find my rulebook right now.

Silly rules question: Does a unit that rallies count as moving, stopping it from firing heavy weapons/halving the range of rapid firing weapons and can it assault (or shoot at all) on the turn it rallies?

Yes, when you rally, you make a 3" move in any direction that counts as your movement for the turn, and all the other limitations of having moved that turn. Unless you're marines, I think.

Edit: just checked, yup Marines are super special awesome, ATSKNF means that they auto-regroup and act completely normally. Fearless+ indeed.