The expressions whoever and whatever are used to express surprise or difficulty in believing something.

Who ever is that cute girl with Peter?
What ever are you doing there?
How ever did you manage to solve that problem? I couldn’t.

Note that these expressions can also be written as single words: whoever, whatever etc.

In an informal style, it is common to use on earth instead of ever.

Who on earth is that cute girl with Peter?
What on earth are you doing?
How on earth did you manage to solve that problem?

The words whoever, whatever, whichever, however, whenever and wherever have similar meanings to ‘it doesn’t matter who / what / which etc.’ A word of this kind acts as a subject, object or adverb in its clause; it also acts as a conjunction joining its clause to the rest of the sentence.

Whoever comes to the door, should be asked to wait.
Whoever answered the phone was very rude.
Whatever you do, I will always love you.
You are free to spend the money on whatever you like.
However much she eats, she never gets fat.

You can come whenever you like.

Whenever I go to Singapore, I visit my sister.
Wherever you go, you will find Coca-Cola.
You can do whatever you want.

Note that whomever is not used in modern English. Whichever and whatever can be used with nouns as adjectives.

Whatever problems you have, you can always come to me for help.

Whenever can mean ‘every time that’.

Whenever I see you, I feel happy.
I stay with my sister whenever I go to Singapore.

In an informal style expressions like whoever, whatever, whenever etc., can be used as short answers.

‘When should I come?’ ‘Whenever.‘ (= Whenever you like.)
‘Tea or coffee?’ ‘Whichever‘ (= I don’t mind.)