When I transplant any of my vegetables I always bu...

Yes, I see people that grow huge trees bury the plants up to cotyledons, it can stabilize stretchy plants. I think I'd be hesitant to bury the stem if it was already completely woody at most places as that could introduce wetness to the wood, and just like with cuttings, it's harder to propagate roots from hard tissue. You can apply some rooting gel/powder around the stem to encourage the growth of roots right before putting the final bits of soil. It's best to do this in early vegetative stage.

Yup. I've seen ppl Bury there's right up to the little tiny leafs at the bottom, no i can't think of their name but you know what I mean. The little leafs before your 1st set of fan leafs. Anyways, if you got a big pot you can surely go down a few inches. Good luck

Certainly can, the buried portion of the stalk will sprout roots eventually and it also helps to stabilize the baby plant.