So how does the summoning process work for lesser Daedra, exactly? Is their essence being drawn through, with magical energy being expended to provide them with a physical body in the mortal realm? Or are you just snatching them up from Oblivion with everything intact? And is there any precedent for Daedra inhabiting other vessels when they're summoned, such as corpses or by possessing living bodies?

Hmm, you might like to read the book "I was summoned by a Mortal" it's a book written by a Dremora in Oblivion about their perspective of being summoned by a mortal.

...and sometimes you can summon Daedra as armour pieces, but not if you live in Skyrim.

The second part of your question is answered by necromancy. Or at least an aspect of it. Most of the times necromancers summon lesser daedric spirits and imbue them in the corpses to reanimate them.

Depends. Bound weapons and armor are lesser Daedra for instance, so twisting their forms to a certain degree is feasible. However, we don't know how low on the totem pole they are, and whether or not the entities being summoned even have a corporeal form handy. Good luck trying to force a Dremora to take that kind of form.

But as to the question of whether or not a "body" is being constructed for them through a spell, or they're being plopped in from point A to B...the two might not be mutually exclusive for the Daedra in question. Physical destruction is fairly important to unbound Daedra, but otherwise negating a particular binding banishes them outright.