Just curious, if for example Wedge Antilles has Marksmanship upgrade, which requires an action to perform hits an asteroid or another ship and forgoes his action, does this mean he cannot perform marksmanship? Seems right, just checking.

Yes that is correct

As mentioned above, you are correct. In general, any upgrde (or critical damage) card that gives you an action option works just like the actions in the ship's action bar.

However, another ship or ability that grants a ship an action, can still be given even if the target ship cannot perform an action itself?

That depends - if a ship has a stress token, it cannot perform actions at all, from any source.

If it hit a ship or an asteroid, it just skips its "Perform Action" step, which means that if another ship gives it an action, it can take it.

That is the impression I was under as well, thanks for the clarification.