Guild Wars 2 – Meaning of the New Icon in Some Skills

As the Wiki entry you linked explains, every time an opponent reduces your life to 0 you go down and have a bar that shows your remaining consciousness which gets lowered by time and attacks and increased if you get revived or call for help (the 4th skill). If you get revived or manage to call for help long enough, you get back into the fight. If it's empty, you are completely dead and can only get revived by another player or respawn at a teleport point.

The starting consciousness gets reduced by the death penalty. White means you start at 75%, Yellow 50%, Orange 25% and with red you die immediately, no call for help or rock throwing possible.

From playing with a dual dagger elementalist, I believe that sigils which proc 'on critical hit' are tied to the weapons skills, so you're correct in assuming that the life stealing will only proc when using the first three skills.

Correction: According to this thread: http://www.guildwars2guru.com/topic/43566-weapon-sigil-questions/ Critical Hit sigils should fire regardless on the skill used, even utility skills, so as long as the weapon is equipped, the effects should be active.

I haven't used the 'on critical hit' sigils too much, as I tend to rely on the 'on weapon swap' sigils, so I could be wrong.