I've seen lots of people saying that you can in fact get robbed, whilst others say its completely BS. I need a straight up official answer because this has been lingering on my mind for some time now.

Not unless its through some NPC glitch or something. The phrase, "NPC's are stealing from me" was a comical way of explaining that items would go missing because people were using unsafe storage in their homes back in the early days of Oblivion. The phrase could even be older than that, but I first saw it mentioned during Oblivions release.

No, but sometimes your weapon plaques "eat" a weapon. I really miss Ghostblade; it was so cool looking.