I have a Jade and have 3 questions related to it.

1) I am cutting the trunk back to thicken it. Can the plant get the nutrients it needs to grow with no leaves?

2) What type of soil would you use to propagate a stem?

3) I've seen pics of Jades with leaves growing from their trunks? Is this species-specific or can you 'force' this type of growth?

I know these are basic questions and I appreciate your time!

1
If you remove all leaves, it will push out new leaves from old energy. When new leaves form, it will start to photosyntesys and push out new roots.
If you remove all leaves + all roots, let the cutting dry for two weeks, without putting it in soil. Within those two weeks, it will push out small roots, when you see them you can pot it up. Leave it like that without watering it for at least one more week. If you see shrinking wrinkels in the trunk because it is losing water, mist it a few times but not the soil.
2
Free draining soil, soil that does not stay wet for a long time.
3
At all old leaf points there can grow new leaves or branches. So if you remove all leaves or branches, new leaves will grow on those spots.