"кто как" = "каждый действует не так, как делают все", "каждый решает проблему по-своему".

This phraseologism has some 'unwrapped' colloquial variant: 'кто во что горазд'.
If you want to wrap in the words situation, when group of people trying to cope with some problem and everyone do it by his own funny handicraft way — it is "кто во что горазд".
In "кто как" this strong funny aspect commonly absent, by it seems to me tha your friend wanted to say something like that =)

«и кому как удается и "выкручивается".»
This strange syntax is not because he "forgot" to properly conjugate the verb. It is just ellipsis, some words have been omitted:
«и кому как удается, тот так и "выкручивается".»

The meaning of "выкручиваться" may be more clear, if try to reconstrust literal meaning. "Выкручиваться" = "крутиться, пытаясь тем самым освободиться, высвободиться". Prefix "вы-" = "покинуть". If you keep your cat in hands (and espeсially if he on his back!) and cat does not want to be keeped, he tryes to weasel out and makes some frantic rorational movement. This is it.