Does the number of corpses affect research?

In UFO Defence - unlike in EU2012 - corpses are never needed for secondary R&D once they've been autopsied. You can freely sell all but one corpse (or, if you've already autopsied one, all of them). Indeed, this is a major source of income earlier on, although selling unwanted UFO components and weapons generally outstrips it by the end of the first year.

Live aliens are a different story, since you can only interrogate each one once, but interrogating multiple live aliens of the same species and rank can give you new research each time - for example, interrogating a Medic will get you information about other alien species, and an Engineer will get you UFO data.

You only need one corpse of each species.

Live prisoners, now...