So what would happen if an animal used the Animal Key?
They turn human. That's how Bode could come back to life despite his body being cremated.
How come the whole "Dodge looks like a corpse in mirrors" thing never came up again?
He used the wellhouse key. Seems like that turns an echo into a real human being.
The Echo Key only brought him back - the entire plot of Welcome to Lovecraft explains that Dodge can't actually leave the wellhouse, and requires the Anywhere Key to escape, which is why he eventually steals it from Kinsey's bracelet to finally escape.
If Dodge goes through the wellhouse door in his current post-Clockworks form, will the soul of Dodge and the parasite be destroyed and leave an empty body, or will nothing happen?
The former. Rufus manages to snag Dodge!Bode once the latter's plan turns to shit, and forces him through the Wellhouse door. It evicts Dodge but leaves Bode empty.
If Rendall Locke wanted to get rid of the Omega key, why not just melt it down?
How is Tyler Locke able to make a key that does exactly what is needed? I mean, for that matter, how are any of the keys made with a specific purpose in mind? Can you just make a key that does anything?
There's a brief scene where Duncan shows him the basics of blacksmithing. The same scene shows a journal from a previous keymaker as well as texts on period-appropriate metallurgy. Even then, the key that Tyler forges has a very simple effect with a lethal side effect - it doesn't work very well.
Why is the giant key giant and wooden? Firstly, the keys only work due to demon metal so the wood is entirely stylistic. Secondly, it would be way more convenient if it was normally sized.
The keys either require or adopt symbolism in their design to show their effect: the genderbending key shows a male and female face, the shadow key shows a candle flame, the echo key looks like the well, etc. The giant key's size may be a necessary accommodation to cause its magic effect.
It could also be purely practical. They probably made the original key at "regular" size, then used it to find...tiny "regular" size keys are very hard to use as a giant (assuming the key, like most, requires a turn to undo the effects). So they added on a giant sized wooden key/remade the key with Whispering Iron and wood/thought of this problem beforehand.
If no adults can understand the keys, how does Mrs. Locke immediately figure out how to use the fixing cupboard/key?
Nina is drunk at the time. Later she's able to hear ghost-Bode while drunk. Perhaps drunkenness bypasses the rules preventing adults from recognizing magic, perhaps because the rule is tied to general adult inhibition.
As Erin Voss explained about the Riffel Rule: "No one who enters the front door of Keyhouse as an adult can see the power of the keys. Not directly. ". My guess is when an adult is drunk, they can see the power of the keys indirectly.
I get that magic is supposed to help, but with the number of high school students and other people who died in that last story, how could anything go back to normal? I mean, a federal officer among many, many others dies under odd circumstances and more than one student dies with odd metal leaking from their orifices. It's all well and good that the children forget what happened as they get older, but that doesn't stop it from having happened. For that matter, after the original 1980s tragedy, it's hard to believe more didn't come of it (at the very least the cave seems like it would have been dynamited shut).
Nina literally sees Bode's head open in Head Games and notices but doesn't really react. The rule blocking adults from remembering magic apparently works in real-time to prevent them from recognizing it as odd in the first place. (Rendell claims it only works on people who pass through the door, but he may be wrong on the details.) It's a safe bet that adult investigators didn't even bother to write down the magic-evident details either in the 1980s or now.
The cave may have been preserved due to its past military utility, either for future use or because of sluggish bureaucracy.