1) If a zombie's instruction is protect this item from harm and that item is perishable, what does the zombie do when that item begins to rot?
A zombie won't see rotting as a harm. (Either because he's too dumb to understand this slow process, because he won't know how to prevent it, or just because, as a rotten zombie, he sees it as the item becoming prettier and more perfect, choose the reason you prefer, the last being not so annoyingly serious as Ravellion's answer).
2) If a ghoul or ghast sees an orc with a pie does it eat the orc or the pie first?
Ghouls and ghast eats corpses. They would kill the orc, wait a bit for it to rotten suitably, and chew it. If they left enough orc bits for him to raise as a new ghoul, that last one would not eat the pie out of religious convictions, having been a pie-defender in its former life.
If your pie is a rotten-corpse-meat-pie, however, they may be interested in it.
3) If a vampire ate regular food, what would happen?
In the Goff game V:tM, he pukes. But in D&D, you could rule that he would then use his undead stomach to produce regular poop.
4) What if vampires are like the people from Death Becomes Her and do not heal?
I don't know this book/movie/opera/play/music/adventure, but if vampires have no way of regenerating, they'll either...
- Be finally destroyed forever; or
- Be finally physically destroyed forever and linger as a ghost
... depending on whether they are cursed by deadlife (fake life) or undeath (unnatural energies possessing the remains).
5) If a lich accidently ate another lich what would happen?
Trick question. Could a lich really eat another ? Accidentally ? There are flylich ?
Assuming we've got, like, a dracolich and a halfling lich, and the former gulped the latter (the reverse would be funny too) without noticing it, then you would have an irritated lich falling through the ribcage of the other lich. Unless the eating lich has some sort of clothing. Because they are usually pretty much skeletons. Their digestive system, when the lich is still fresh enough for it to exist, is not functionnal.
6a) If you resurect a dead vampire do they turn into the human they once were or back into the vampire?
You can't raise undead to life; however, once destroyed, you can bring them back to real life. It's what the rules says.
6b) If they become human again do they remember being a vampire?
Your choice. The target of a raising spell will only have hazzy, fugitive memories of his life in the outerworld, but the rules says nothing about memories of unlife.
Since undead are all "mindless" in a way (even intelligent undead like vampire), that means they lack a part of their soul. The part that must be wandering between the outer plane of the afterlife, and the material plane where the rest of its essence is trapped, unable to join either as long as it's not whole.
When raised, the soul is joined again.
You could either say the vampire's memories are swiped out (like its alignment, the raised person will take his former alignment back, rather than the vampire's CE), because only that of the "living soul" matter...
... or that all memories are merged, and the raised person will now live in angst and all that stuff (if good, depressed about the evil he's done, if evil, depressed about the power he's lost).