Do I need to draw the beam directly across the enemy crew member, i.e. exactly over where they are stood, or does just damaging the room they are in also hurt any crew in that room?
Based on observation, both sorts of beams behave the same way. Crew members are only damaged in the path of the beam. It's hard to test this as you only see health bars right after a hit, and sometimes yhou need to follow up with another weapon and try to eyeball the results. I thought I had confirmed that regular beams damaged crew members regardless, but I just did some more testing and it seems I was mistaken.
Bio-beam definitely does not hurt crew people not directly in the path.
I was curious about this as well.
Beam weapons must cross the hit-box of units in order to do damage to them.
As an extra note, the beam must cross where the unit is at the time,