1a and b are both not possible.
She pretends to be an actress.
‘feigns’ doesn’t really make sense at all in this sentence.
3b. Pretending to have a headache…
If the point of these sentences is to find out whether the words ‘pretend’ and ‘feign’ are synonymous, the answer is no, not always. ‘Feign’ has a more precise meaning than ‘pretend’. It can only be used in certain situations.