For example, if I were trying to cast a spell on a dead creature who previously had spell resistance, would it still apply?
This will depend entirely on whether your DM considers corpses to be objects, or dead creatures. There is an implicit assumption in the rules that you won't cast magic on corpses other than magic made specifically for interacting with corpses. The rules for death, and what happens to a character's corpse, are very poorly defined, and it's pretty clear that the designers weren't really thinking about the mechanics of death when designing the system, assuming instead that players would be able to figure it out as they went along.
Thus the "object or dead creature" dichotomy. If a corpse is an object, then it doesn't have spell resistance, since it's an object. If the corpse is a creature that happens to also be dead, then it keeps it's spell resistance.
There is strong circumstantial evidence that corpses should be considered objects, but it's never explicitly called out in the system. See this answer for more details on that point.
Honestly though, it could go either way, from a rules point of view. If your DM (or you, if you're the DM) thinks that it makes sense (either by the incomplete rules or by the feel of the setting) for corpses to keep their SR, then go ahead. As long as the ruling is consistent, either way has some support in the rules.