Not offering some, asking for some.
More than few times, I managed to hit my target while sneaking, crit, and the target didn't see me, he/she was rather looking around for me with typical "Is someone there!?". Then again, in most cases it's usually hit>detect as it was ment to be.
Let me just add in some cases I've hit the target on the move, in front, and I still remained unseen.

So can anyone tell me which factors play the role in this. Also, since I am not able to play at this moment and cannot test this out, is dual dagger power attack while sneaking always crit with both weapons, and does the whole combo make crit, or is it rather first one to land > detect?

No idea about the dual dagger power attack, but regarding what affects detection, http://www.uesp.net/wiki/Skyrim:Sneak#Remaining_Undetected should be useful