The game rules for Dogs in the Vineyard describe conflicts in terms of rolling in one Trait or Belonging on a given See or Raise. They don't explicitly allow or prohibit players from rolling in more than one.

In games I've played, you'll sometimes get a player who rolls poorly with his Gun wanting to immediately follow up by rolling his "Good Marksman".

I'm inclined to allow players to roll more than one Trait or Belonging for a single See or Raise, but only if:
1. they go well together (Gun + Good Marksman)
2. both are rolled together, and not one at a time (shoot, that was a bad Gun roll, so I'd better roll in for Marksman)

But I'd love to get an official ruling (or have my reading of the rules corrected by someone in the know).

Rolling both a trait and a belonging in on the same raise or see is fine if the raise or see brings both of them legitimately into play. A gun + "I'm a good shot" is a perfect example - when you shoot someone, yes, you should roll both. I'm more reluctant about rolling two traits at the same time - "I'm a good shot" + "I'm good with horses," for instance, when you take a shot from horseback - but I'll go along with it when it makes sense.

I never worry about your #2, provided that #1 holds. Not legit: "I shoot him! I roll my gun's dice ... dang, those are crap. I'm going to bring in 'I love to sing,' I guess I'm singing while I shoot him." That's a no, knock that off.

-Vincent