Whatever and Any

I'm having trouble explaining the difference (and similarities) in usage between "whatever" and "any": when they can be used almost interchangeably, when they cannot, etc.

I've compiled a basic list (below) of the usage with the help of a dictionary, and am looking for feedback.

1) as a relative pronoun
Ex. You can eat whatever you like. (Here, "anything" (meaning "the possibilities are endless" can replace "whatever" (meaning "it doesn't matter what").)

2) as a demonstrative adjective
Ex.#1 We'll be ready at whatever time you get here. (Here, "anytime" could replace "at whatever time.)

Ex.#2 If the bus doesn't come for whatever reason, call me. (Here, "any" could replace "whatever.")

3) as a question pronoun
Whatever do you mean? (cannot use "any")

4) as a conjunction
We must stay together whatever happens. (cannot use "any")

Any feedback, particularly regarding 2), where "whatever" and "any" are used as demonstrative adjectives, would be particularly helpful, as would any exercises related to this topic.

Thanks.