Sometimes in the game i saw NPC sneaking and stealing, sometimes they are busted by NPC but they never get caught by guards.

In Skingard i saw the hooded man, Surille i think his name sneaking around NPC at graqe farm.

In Cheydinhal while i am doing the corrupt guard quest, there is a Khajit, sneaking and stealing from a guard in guard barrack, the guard get angry, but not arrest him. Then the Khajit sit at the guard dinner table, drinking and eating, acting like nothing happen. I talk to him, and he's just chat normally.

Is this normal or just random, or it is some kind of a quest or something?

Are we ever get robbed by thieves unaware?

We do not get robbed by thieves unaware in the game.

I have seen both City Swimmer (Bravil) and Shameer (Skingrad) steal something and get killed by the guards for it.

Oh, i have no worry getting robbed then

I never see anyone got killed by guard because of that, and the Khajit at Cheydinhal is funny, he get caught in guard barrack, then he just drinking and eating there like nothing happen

Oh neat! I don't see NPCs steal and get caught much, but it is nice to know that sometimes they might be able to live tell about it.