Larch trees do not generally backbud, but it seems that buds form on places where there wasn't new growth.... how is this possible? like there were buds on very thick branches closer to the trunk that opened. or were these new growth trimmed way back to the base of the shoot? This is my first season working with larch, so I'm figuring out how to trim.

or do buds that didn't open one year open sometime in the future?

I am not sure I understand the question. Because larch do nor reliably backbud (You do get the odd one here and there at times) people take great care keeping the buds neer the trunk.

Not all buds extend into branches.

I'll try and rephrase: Buds only form on new shoots? if not when and where do they form?
do buds that didn't open in one year open later sometimes?
A few of the buds on the trunk of the tree seem to either have back budded or opened at a later time... I'm not sure why.

If I wanted to trim a branch in the winter, would I trim it back to the bud closest to the trunk?

In some cases you get the odd bud here or there. A hard prune may cause some buds to show. Maybe that is what you are seeing?

Normally if a bud does not open, it is a goner. As such, I would never prune to the last bud, but rather leave 2. You can always prune back to the first if you see healthy growth in spring.