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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.
Comments  
I think the answer lies in the parts of speech inherent in each of them.

whatever: adj., pron., counj.
any: adj., pron. adv

Adjective: They both function as an adjective, therefore, they are interchangeable.
Ex)You can take whatever book you like.

Pronoun: Broadly, they are both categorized as pronouns. But their subcategory is
different.
whatever: interrogative pronoun - "What(ever) do you mean?"
any: indefinite pronoun
This difference in their subcategories makes it impossible for them to be
used interchangeably.

Conjunction: 'any' has no function of a conjunction, while 'whatever' does.
Furthermore, [whatever + clause] can be either a noun clause or a
concessive adverbial clause.
Ex)You can take whatever you like. (noun clause)--interchangeable as
both 'whatever' and 'anything' share a noun function.
Ex)Do your best whatever you do. (adverbial clause)--not interchangeable
as 'any(thing)' has no adverbial function.
'any' does function as an adverb, but mostly is used
before comparatives.
e.g. any longer, any more, any further, ...

Best wishes.
Thank you. This is very helpful.