Normally an undead (if made of flesh) will have an expiration date after which it won't be able to function anymore.
Not necessarily true. This heavily depends on how undead are made to function in your world. The "expiration date" is usually only common for:
- Reanimated corpse zombies. They might continue to decompose yet still move. So at some point it will be physically impossible for them to continue obeying commands.
- Undead created by a time limited spell. In this case it might be a zombie or anything else and they have an "expiration" which is the time the magic that animates them ceases to function. There is otherwise no "natural" end to these creatures.
So, undeath is not a simple state. Everything has exceptions, of course as there are numerous depictions of the undead. In particular zombies might be reanimated indefinitely. The natural decomposition process halted. If they fight, they'd accumulate wounds and won't heal them (not without some help) and breaking the spell that animates them might end them but otherwise can exist forever.
There are even mundane ways to make a durable zombie. Well, mundane in the context of being able to use magic to make move. One variation is the mummy. It is still a cadaver animated by magic. However, mummy preparation preserves the corpse and so they are more durable.
However, even works without overt magic yet feature zombies might have the zombies exist forever. Many zombie apocalypse scenarios depict the undead as existing A LOT longer than they should have. In the real world the body decomposition works quite fast. A cadaver left out for a month would not be very useful to anybody. After a year, it's not even going to be much of a cadaver. Yet works where somehow zombies exist still show them move around and attack people for years. Even change of seasons should have destroyed them - summer heat is very unkind to dead meat. Winter frost also leads to damage. Not to mention microorganisms as well as macroorganisms taking the opportunity to feast. Assuming a zombie exists, it should be constantly surrounded by flies at the very least but also all other manner of creatures that eat carrion. Yet...that's not usually the case.
They are undead creatures but are capable of healing and regeneration, something a corpse shouldn't be able to do. And that brings the problem "how are they undead"? They regenerate so they don't decay. They can move like a living being. In some cases they can reproduce.
Aside from how your undead function, you are now mixing this with vampires. And vampires in folklore as well as fiction work in drastically different ways. The most common thing between different types of vampires are that they are medically dead (no pulse, organs don't need to work, etc) and they feed on the living (doesn't even need to be blood). Yet even these have various exceptions between depictions.
There is simply no one way to talk about vampires. Some might be undead, others might not. Yes, some might be able to regenerate, others might not. Some might not decay, others might not. Some might reproduce, others might not. The whole reproduction thing is a mess, as well - some can reproduce sexually but it still varies - perhaps they can have a child with a human, or perhaps they can only have a child with another vampire. Or the reproduction is limited to turning somebody else into a vampire.
Still, if we take the more common depictions that have vampires which don't decay, regenerate and keep their appearance, then it's actually not really that much that they "heal" in the biological sense. Usually these vampires are captures in stasis - their appearance never changes, they remain the same throughout the ages. So, they don't "regenerate" as much as they return back to their normal state.
If a wizard were to cast a healing spell on a regenerating undead, would it even have an effect? Would it heal the undead or damage it? Or is the undead now reanimated so it's fully alive?
It depends on how magic works in your world and how your undead work:
- Healing magic does help the undead.
- But then it's a general purpose healing magic that can restore anything similar in biology.
- Healing magic simply fails.
- In that case, it's helping the living to regenerate faster but not the non-living.
- Healing magic harms the undead.
- This plays on the opposition of life and death and sometimes even good and evil. Opposites harm one another and to "heal" a corpse would be to return it to it's real non-living state where it doesn't move or act. Conversely undead healing means might harm the living.
Overall, there is no One True Way to depict the undead. Because they don't actually exist, thus we can't really say how they function or not. Each work implements their own rules and might even break them at times. Almost no two works have undead or vampires work the same.