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.