Do you have to choose which power you're emulating at a time with Lantern's Will? I thought they all went off seperately, but recently, at a tournament, I was asked which option I was using. I thought that, for example; when being shot at, deflection would trigger, raising the defense and, if the attack was succesful, toughness would kick in, reducing the damage.

Which way is it?

They are both passive powers. You don't have to do anything. They all just happen.

By the wording it appears that he can use them. by this i mean, when GL is the target of a ranged combat attack, his defence is modified by +2. when an attack succeeds it is reduced by one, and when he takes a non-free action when he has one action token, he does not take pushing damage. You dont need to declare that you are choosing one or the other for the duration of the attack. if that was the case it would have that worded

Short answer...No.

Joh-Marko is correct, you can use all the powers. As far as I am aware, anyway. Good question.

You do not have to choose with the Lantern, as none of those powers require you to do anything.
They were apparently applying the "Flash can use phasing/teleport and charge" rule to that power, and it simply isn't appropriate.

You were right, ESD then Toughness. Willpower on your turn, or if someone tried to Incap. you, you could also use the WP to not take Pushing Damage.

Right, for example, let's say a brand new Superman piece has a power called Son of Krypton which is listed below:

When Superman is attacked at range, as he is targeted, the Shape Change would be rolled. If that roll fails, the opposing player then has to hit Superman's value with the ESD +2 bonus. Let's say the attack is successful, Superman then rolls his Super Senses. The Super Senses roll fails, so now Superman is hit and then says he'd like to use the free knockback portion of the Combat Reflexes. Then Superman would roll his Impervious to see how much damage he would actually take, and how many squares he will be knocked back due to his Combat Reflexes option.

Also note, that after the Impervious roll was failed, Superman could then use Protected if it had been assigned, and since the special power granted him Willpower, he would not take a pushing damage if he already had one token!

Now when Superman goes on offense, his options would be much more limited, as he would have to choose between using say the CCE, RCE, Hypersonic, Flurry, or Charge, as they all require a separate action to activate. In this case though, Superman would be allowed to Charge and then Flurry due to the wording of the PAC for Charge and Flurry.

So the same could be said about Sinestro's Might?

Yes is the same.

SINESTRO'S MIGHT!: Sinestro can use Energy Explosion and Ranged Combat Expert. When Sinestro uses Energy Explosion, damage dealt is penetrating damage.

So in this case you will choose what you want to do, but not the two powers at the same action.

and of course Let Those Who Try to Stop Whats Right