I'm focusing on Quake, but I'm curious about the powers in general. Can you choose not to use them? with some it seems you can; TK, Incap. With others it seems you can't( earthbound). Can you choose not to use your powers?

Page 18 of the rulebook:
That should clear it up for you, but if you still have questions after that, feel free to ask.

Harpua is right on.

Learning the proper terminology will help in understanding how all powers are used.

To answer your questions explicitly:

When your character possesses or can use Quake, you have the option to give the character a close combat action to activate it; you are not forced to use Quake with every close combat action that character makes.

Same deal, just because the character possesses or can use TK doesn't mean you MUST give the character a power action to use it.

Same thing.

There is no named action required to activate Earthbound - it just exists as is. So while a character possesses or can use Earthbound, you must follow Earthbound's game text to "nerf" that character.

ok, So saying "give this character a close combat action" is essentially saying you MAY use this ability by giving them a close combat action, not WHEN you give them a close combat action, this stuff happens.

The definition I have for quake doesn't explicitly have the word "may" which is where my doubts were coming from. People have been playing it as optional, so I assumed that was the case, but I thought I would check.

As per the rules above: "Some game effects require that a character be given an action. These effects only activate when the character has been given the action specifically to activate the game effect. The game effect then overrides the normal activity of that move, close combat or range combat action."

Quake is like that.

You give the character a close combat action. This is essentially paying a cost to activate something. You then have to choose what that cost is paying for.
Are you giving that close combat action to the character to pay for using Quake? Are you giving it to pay for using Haymaker? Are you giving it to pay for simply giving a vanilla close combat attack?

But, yes, if the effect says "Give this character a {type} action to..." then you don't have to give it that action.

Yes. But be sure to read the powers carefully, because there are powers that activate WHEN you give the character a close combat action and those powers activate any time you give the character a close combat action for any reason.

Agreement with VP. Energy Explosion will activate anytime you make a ranged action that deals damage. Likewise Precision Strike will activate for any attack. Conversly when you give a close action you may activate quake if you have it or you might just make a vanilla attack.

Just to be clear on energy explosion, it may technically activate anytime you make a ranged action that deals damage but whether or not there is an area of effect is up to the attacking player.

Right. Just like blades always activating for a close action but having the option to roll.