Page 646 - Practical English Usage 3ed - Michael Swan, Oxford

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Whichever and whatever can also go with nouns as determiners. Whichever room you use, make sure you clean it up afterwards. Whatever problems you have, you can always come to me for help.
Ifyou change your mind for whatever reason, just let me know. clauses as subjects or objects
A clause with whoever, whichever and whatever can be the subject or object of the verb in the other clause.
Whoever told you that was lying. (subject of was lying)
I'll many whoever I like. (object of many)
Whichever climber gets to the top first will get a £5,000 prize. (subject of
will get)
I'll take whichever tent you're not using. (object of take) Whatever you want is fine with me. (subject of is) Prisoners have to eat whatever they're given. (object of eat)
whenever = 'every time that'
Whenever can suggest repetition, in the sense of 'every time that'. Whenever I see you I feel nervous.
I stay with Monica whenever I go to London.
whoever etc . .. may
May can be used to suggest ignorance or uncertainty.
He's written a book on the philosopher Matilda Vidmi, whoever she may be. She's just written to me from L/andyfrdwy, wherever that may be.
leaving out the verb: whatever his problems
In a clause like whatever his problems are, where whatever is the complement of the verb be, it is possible to leave out the verb.
Whatever his problems, he has no right to behave like that.
A serious illness, whatever its nature, is almost always painful.
After however + adjective, we can leave out a pronoun + be.
A grammar rule, however true (it is), is useless unless it can be understood.
informal uses: short answers
In an informal style, these conjunctions are sometimes used as short answers. When shall we start?- Whenever. (= Whenever you like.)
Potatoes or rice?- Whichever. (= I don't mind.)
Whatever is often used to mean 'I don't care' or 'I'm not interested'. This can sound rude.
What would you like to do? We could go and see a film, or go swimming.- Whatever.
Or whatever can mean 'or anything else'.
Would you like some orange juice or a beer or whatever?
Ifyou playfootball or tennis or whatever, it does take up a lot Oftime.
whatever meaning 'at all'
After any and no, whatever can be used to mean 'at all'. Don't you have any regrets whatever?
I can see no point whatever in buying it.
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