If a character is Hidden (as it is defined in The Rules of Hidden Club), having done all the necessary skill checks, and is in a Totally Obscured area, can he perform a light thrown attack while remaining hidden? Also, can his hidden condition give him combat advantage when performing the ranged attack?
TLDR: Light thrown weapons interact with stealth/hidden exactly the same as any other kind of weapon/implement attack does.
No, you will not be hidden after you attack.
From the Rules Compendium, p153:
After the attack resolves, you will no longer be hidden unless you have a feat or use a power that explicitly allows you to remain hidden after the attack.
Yes, you will have combat advantage on the attack.
From the Rules Compendium, p152:
From the Rules Compendium, p221:
If you're hidden, you're invisible. If you're invisible, you have combat advantage against anyone who can't see you. You don't lose hidden until after your attack is resolved, so you have combat advantage for the attack.
Oblivious Sage is correct, also there are certain feats (Mark of Shadow for example) that will keep you hidden even after you attack so long as the conditions are met.
Rogues Specifically can also use powers like Gloaming Cut (Martial Power 2 pg 57) to attack then make a check to become hidden again.