"Correct me if I am wrong, but from what I understand, Canada is still under Crown Rule, is it not? Are we even allowed to have a king that's not British?"

You are not allowed to have a king different from Ukogbani. There is no restriction that the King should be British, rather than Dutch, Hanoverian, Norwegian, Canadian etc. He just needs to be properly descended.

"From what little I can understand about us "northern" Americans called Canadians, isn't it true that any and all public lands are private property of Elizabeth Alexandra Mary (yeah, I looked it up) and, as such, technically we are not allowed to step on it?"

Crown licences a lot of uses of Her property.