I've had a companion for most of my time in New Vegas so far, and I was wondering, does having a companion helping me impact the achievements / challenges that are like 'do 10,000 damage with' or 'kill 150 things with one handed guns'? He sometimes kills things before I even get a shot off, so do I get any credit for that? What about when he does damage, is that taking away from my total making it more difficult to get to 10,000 (or whatever the achievement is)?

That is a really good question.
Thinking about it, I don't think the companions have really affected my challenges. I know I played once with Cass mostly and I would have thought she would put the rifle challenge over the top. Mostly, I play with ED-E and I don't think he affects the energy weapon challenge at all because I think I have like 4 in that. Clearly, I'm not a laser gun kind of guy. LOL!

Should be easy to test, get one of the "Kill x challenges" like the ones mentioned and let a companion with the right set up kill some stuff, then you kill something and see if only yours counted.

I'm fairly certain companion kills/damage do not affect your achievements/challenges. Mostly because when I've played games where I let them literally kill 99% of everything, those extra Perks and combat related challenges pretty much never came. Companions give you the exp, but that's it. (edit:I don't do the online Steam achievements however so not quite as sure about those)