It depends on context. Either you are saying it has never happened in the past, or you are saying it's a general truth.
Taking your second example first: it is a general truth that your friend doesn't pay tax, so use the present tense:
My friend never pays any tax.
(Note it's pays and not gives pay. "Gives pay" is not natural English.)
With your first example, the idiom is to have or to throw a party, not to give a party. Throw usually takes an indirect object:
My friend just threw her mother a surprise birthday party.
While have uses for:
My friend just had a surprise birthday party for her mother.
In this case you're talking about past events up to the present moment, so use the past tense:
Now I feel bad. I never threw my mother any parties. I should throw one this year.