Anything that isn't the current situation...
Rianna's still curious about the glimpses of visions she had seen, on Taneshla and Bespin. She still wants to know what they are and figures it'd be safer than working herself into a panic, and she doesn't want to admit to what she wound up doing on Bespin.
No, but he did apparently have a dozen other plans as well...maybe it would have given away something.
Also curious how he knew where she was from. I don't know if Rianna even knew that - somehow I doubt that sort of thing is public record.
Essentially, though, Rianna doesn't know why Rand felt the need to hide it from her. She's not entirely sure that the vision even existed in the first place - if you can hide a vision from someone, surely you can plant a bit of one in their mind? But, really, she doesn't understand why Rand does anything he does. Or why he was even so set on her in the first place.
It may not be public record. The Jedi Archives would certainly have that information.
It is clear that Rand is powerful in the Force enough to cast his shadow over others. You aren't certain that the Force works that way, or that even the most powerful Sith Lords were able to do that.
Though again, studies in Jedi Lore aren't your strongest.