Another big house game led to another round of questions. Any help would be appreciated.

1. A giant fig can attack two squares away, correct? Is that considered a close combat action, ranged, or either I choose? Can I use RCE despite being based? What if the basing character is two squares away?

2. Can a standard figure use ranged combat on a giant two squares away? Can I use it if they are in the square next to the giant fig? And, can I use RCE? I know that I can't attack someone else with range, I'm asking specifically can Bullseye attack say Chemo from two squares away, adjacent to the big fig Chemo?

3. How does quake work with giants? It's the two square radius, right? And poison only works in one, correct?

4. Can I TK a giant figure? Can I TK Sinestro or Sentinel?

Now to my Power Cosmic questions:

5: Do exploit weakness and pyschic blast still work? I assumed they did.

6. Are power cosmic figures on a two-out-of-three turns action cycle or can they continually push every turn without having to take a break?

Thanks for any help.

Giant adjacency rules allows a Giant to attack a figure up to two squares away. However, they are not forced to do a close combat attack unless the figure is in an immediately adjacent square to the giant: a figure 2 squares away can be attacked with either a ranged or close combat attack.
Depends a little on the figure as a flier always has the ability to make ranged attacks. However, a non-flying figure can make a ranged attack against a giant if it is 2 squares away from the giant even though the giant can choose to attack said figure with a close combat attack. If the non-flyer is immediately adjacent to the giant, it has to make a close-combat attack.
Correct. Rule of thumb: If it involves movement or the giant's close combat, adjacency is 2 squares, otherwise it's 1 square. Quake is a close combat attack, so the giant does get extended adjacency. Poison is neither movement nor close combat (even though it involves adjacency), so it only works in standard adjacency.
No.
They still apply. Power Cosmic says powers may not be countered (i.e. Outwitted), but PB and EW ignores damage reducers. Big difference.
Unless they have special rules saying otherwise (like Dark Phoenix and Galactus), a Power Cosmic figure may not be given another action when they have two action tokens. In other words, they are limited to acting two out of three turns.

I'll answer these first:

5. Yes, Power Cosmic only prevents powers from being cancelled, but penetrating damage will still work.

6. They can't continually push every turn. Only Colossal and Sentinels can (it's part of their rules, not Power Cosmic).

Let me begin by recommending you re-read the giant rules in the Danger Room rule book. All of these answers can be found there.

The giant's two square adajaceny is in effect for movement and the giant's close combat only. So, the Giant could make a close combat attack on a character two squares away. The giant could also make a ranged combat attack, if it wasn't adjacent to an opposing figure (and remember, since the two square adjacency only works for movement and the giant's close combat, adajcency for a giant's ranged combat is the same as any other character: actually right next to the giant).

Again, the giant's two square adajaceny is in effect for movement and the giant's close combat only. If the character trying to shoot the giant is not actually adjacent to any opposing characters, yes it can shoot the giant from two squares away (since ranged combat isn' covered under the two square adajcency rules). If the character was adjacent to the giant when trying to perform a ranged combat attack (and remember, since this is range, adajcent = right next to), it could only do so if it was a flying character or colossal character (characters that can normally perform ranged combat attacks when adjacent to an opposing character).

Your particular scenario of Bullseye vs Chemo would work just fine because Bullseye and Chemo aren't trying to move and Chemo isn't trying to perform a close combat attack. Therefore, they are not adjacent.

One more time (seeing a trend here? ), the giant's two square adajaceny is in effect for movement and the giant's close combat only.

Quake would be a close combat attack by the Giant. Quake will function with the two square adjacency rules.

Poison is not movement or close combat. It has normal adjaceny rules.

This is part here, more than anything else, is why I recommended above you reread the giant rules. Directly from page 50 of the DR rule book:

Giant characters ignore hindering, elevated, and outdoor blocking terrain on movement. Giant characters cannot be moved by Telekinesis, and they ignore other characters’ Force Blast and Plasticity.

And for colossal characters (like Sentinel), page 51:

Colossal characters cannot be moved by Telekinesis. Colossal figures may make ranged combat attacks when adjacent to opposing figures.

Power Cosmic (and Quintessence) TA prevents powers from being countered. Psychic Blast and Exploit Weakness do not counter powers; they, instead, deal penetrating damage. Penetrating damage ignores damage reducing powers, it doesn't counter them. PB and EW work just fine on PC and Quint characters.

Unless they have some special rules like Colossal figures or MoE TA, all characters must rest when they have two tokens placed upon them.

So, Galactus and Dark Phoenix (colossal characters with PC) could keep pushing. Silver Surfer and Thanos (characters without special rules) must rest after taking a second token.

Thanks! That's why I love the Realms. People here are quick to help!

I just want to point out that the damage from EW and PB is penetrating damage, which means the damage dealt by those attacks can't be reduced by damage reducing powers or abilities, it does not (as several people have errantly indicated ) mean they ignore those effects. The difference is subtle, (and often unimportant,) but can result in things like the AW BFC being triggered, even though the damage dealt isn't actually reduced, to cause an additional click of damage.

To elaborate, since the targets' damage reducing powers aren't ignored they will attempt to reduce the damage dealt, which is all that is necessary to trigger the AW BFC, based on the precident set in relation to a figure dealing 1 damage with AP to a figure with a damage reducing power while AW is in play.
Probably not a life changing difference, but a difference just the same.

BoT