For the book sequels, and the series as whole, see Land of Oz
The Tin Man is so kindhearted that he can't stand to see a mouse killed by a predator...and so he takes out his ax and lops off the predator's head? How does that work?
Well, the mouse's death would be quite painful and graphic, where the beheading is relatively clean and painless, right?
Plus, the wildcat was knowingly trying to kill the mouse (all animals in Oz are sentient, remember), so really, he was saving her from a murderer.
Nick is the kindest fellow...but that kindness extends to protecting the innocent from harm. When innocents (or his True Companions) are in danger, all bets are off. Scarecrow's not much different, but he didn't have as many opportunities to show off the Badass streak.
Just what did the Wicked Witch of the West do to earn the "wicked" title? That is, what did she do in the past (before Dorothy arrived) that made her so feared amongst the populace?
The usual stuff - a tyrannic rule with the help of the flying monkeys?
That's about right. She enslaved the people of Winkie Country. Likewise her sister had enslaved the Munchkins.
According some of the later books, Oz used to be ruled by a line of kings and queens. The last king disappeared and four wicked witches split up Oz among themselves. The Wicked Witches of the North and South were overthrown by The Good Witch of North and Glinda the Good.
Also, she's guilty of accessory to musical theater.
If water is the only thing that can kill a witch, why did that first witch die from having a house fall on her?
Having a house dropped on you is NOT going to leave you in good shape, no matter what else your weakness.
Weaksauce Weakness. They never said it had to be pure water or liquid water for that matter. Even if the house itself is disconnected from the water supply, Dorothy herself being in the house at the time could have been enough. Or more realistically, Dorothy's house lands on witch, causes injury to witch's lungs, and complicated stuff ensues which leads to the wicked witch essentially drowning in her own bodily fluids.
Tornadoes also come with nasty rainstorms in tow, if I recall right. Caught in the rain probably didn't help matters.
Where is it said water is the only thing that can kill a witch?
To my knowledge, only in the "How It Should Have Ended" animation for The Wizard of Oz.
In one of the books, an early one, it says the wicked witches had been dried out as the result of being wicked for so long, making them vulnerable to water. Sort of like living mummies. So you'd expect them to get powdered pretty well by falling farm-houses, too. Now you just have to figure out why evil has a dehydrating effect.
It was the first one - and only said of the Wicked Witch of the West, not Witches or Wicked Witches in general.
Tin doesn't rust.
Could be partially justified, in that one of W.W. Denslow's color illustrations shows the Tin Man's joints are a different color, perhaps indicating that his joints are made of a different metal.
Actually, The Tin Man is made from tin sheets — which are sheets of iron coated in tin, which is what tinsmiths use to make products from. The tin coating prevented the iron from rusting, but the Tin Man's coating may have chipped in places, and — more likely — is probably worn through at the joints.
Volkov's adaptation avoids this by making him made of iron instead of tin, but still.
The Tin Woodman's transformation occured gradually, with individual parts of himself being replaced as they were hacked off by his cursed axe. 1) How do you survive chopping off your own head (or) what injury is severe enough to require completely replacing your torso, but you still survive it? and 2) After the second or third limb, did he not think to just get rid of the axe? (or stop chopping wood for a living?)
1) No-one dies in Oz. 2) Munchkinland was probably in a caste system at the time.
So is the Emerald City made of emeralds after all? Supposedly the Wizard built it out of glass, and that's what the green glasses law is for, but about halfway through the second book all mentions of glasses disappear and the emeralds are treated as real afterwards. Continuity error?
I assume the Scarecrow made it into a city of emeralds.
If Oz is real but is surrounded by the impassable Deadly Desert, how did enough people reach it to establish a viable population, let alone a civilization of five distinct nations and innumerable smaller cultures?
As I recall, Oz used to be connected to the other magical lands. A passing fairy queen made the impassable deserts and isolated Oz from the outside and enchanted the land. They may have been already people living there. The four nations came about when the last King of Oz disappeared along with his daughter and four Wicked Witches carved up Oz among themselves. Later two of the four Wicked Witches, North and the South, were overthrown by Glinda and an unnamed Good Witch. As to the fifth nation (The Emerald City), that was founded by the Wizard after he came to Oz.
Wicked (the book) gave a simpler, Hand Wave-ish explanation: the desert isn't really deadly; that's just a bit of political propaganda intended to discourage foreigners from intruding into Oz.
If the witch melts with water, how does that dirty woman take a bath?
She doesn't. It's why she turned green.
Actually, that's more or less what Wicked said; she rubs oils into her skin.
If there is No Death in Oz what does Munchkinland need with a coroner?
Well, that's one more Munchkin who escapes unemployment — possibly the fact that his job is essentially pointless is less important than the fact that he has a job. There are a lot of "jobs" like this in Oz canon; they're of no practical use to anyone except to let people feel they actually have something to do.
My recollection is that "No Death in Oz" is only true in the books, and the coroner only appears in the film, so there's no contradiction.
More specifically, the "no death" rule was only introduced in the later books. There are actually quite a lot of deaths in Wonderful Wizard, including both Wicked Witches and many animals encountered by Dorothy's company in their journeys.
My recollection was that the "No Death" rule only came into play when Ozma (or the rightful heir) was placed in power. Presumably, this makes the wicked witches even more evil by taking over Oz.