what does this have to do with this skill?
Nothing, they're just letting you know.
how come 'You can take whichever car you want' is correct and 'You can take whichever car you like' is wrong. This is very confusing I think the translation could be better in this lesson.
Report it! Hvad/hvem/hvilken som helst doesn't translate directly, but both of the translations you gave are correct.
want = vil, like = kan (godt) lide
"You can take whichever car you like" would be "Du kan tage hvilken som helst bil du kan lide".
can 'hvilken som helst' be translated as 'whichever' in general?
Yes, you can basically translate all the "[word] som helst" constructions to "[word]ever". A more literal translation would be "which you favour".
There are several correct translations for this, why this particular one?