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So I’m just wondering, do knights pivot at the waist, and if so does this effect their firing arcs?

Technically, they pivot at the waist. Only when you're building the model though, the torso will just fall off if you don't glue it in place. So, to answer your question: no (and no).

I always find it easiest to base the facings for a knight on the base rather than the model. This allows for more dynamic posing and makes it easier for yourself and your opponents during the game - each knight has the exact same facings etc you can determine from the base.