Title says it all.
I wanted to know if I can use power attack with a thrown weapon, like a chakram or even a shuriken.
You can choose to take a –1 penalty on to gain a +2 bonus on This bonus to damage is increased by half (+50%) if you are making an attack with a two-handed weapon, a one handed weapon using two hands, or a primary natural weapon that adds 1-1/2 times your Strength modifier on damage rolls. This bonus to damage is halved (–50%) if you are making an attack with an off-hand weapon or secondary natural weapon.
When your base attack bonus reaches +4, and every 4 points thereafter, the penalty increases by –1 and the bonus to damage increases by +2.
You must choose to use this feat before making an attack roll, and its effects last until your next turn. The bonus damage does not apply to touch attacks or effects that do not deal hit point damage.
No.
Deadly Aim is the feat you're looking for.
Yes and no.
Power attack grants a penalty to hit on melee attack rolls and a bonus to damage on melee attack rolls, so it will only have an effect on melee attacks. Normally this means only melee weapons. You could use power attack with a thrown weapon, provided you at attacking with it in melee (not throwing it, which would be a ranged attack roll), which the chakram allows you to do by making a reflex save an taking a penalty. Shuriken, however, specifically state that they cannot be used in melee, if I recall correctly.