Had a mythos card that stops investigators on taking a focus action and lose all focus counters, but got a mythos of everyone receiving a focus and I was also going against Ithaqua. So I need to clarify focus actions.

Using the Action: Gain a Focus should be a focus action?

What about gaining a focus via a mythos card?

Is spending a focus against Ithaqua count as focus action?

The Mythos card instructs you gain a token, the previous Mythos forbids you from taking focus actions: the two are not in conflict. Simply, you cannot spend an action to gain a token, but you can gain tokens by means of other effects, and if you have tokens acquired this way, you can spend them.