My take on Elayne's formative personality influences is that she was heavily affected by Morgase's attempts to correct her own shortcomings and lack of preparation for the throne. Morgase, whether for good or ill, very much operated on an emotional basis a lot, and the sisters in Fal Dara discussed her attitude toward the Tower and getting Elayne trained as a "more Catholic than the Pope" kind of overcompensation. So Elayne is obsessively duty-oriented, and very rational & logical in her thought process. Note that she usually has reasons for actions other people think of as insane risks, suggesting she is either really quick at rationalizing her behavior (and that she feels a need to justify doing what she wants according to an abstract standard) or that she is really thinking that fast, and has already decided her course of action on risk/benefit assessment. In either case, someone who goes with her brain over her heart or gut.

I think she would have been conditioned to weigh and assess stuff like propositions and courting attempts. Despite her own naivete in certain areas, she tends to dismiss noblemen her own age as boys (Beslan and the Renshar kid from KoD), and she doesn't appear to have any friends among her female peers. I think her upbringing/training/anti-Morgase-drill kept her from getting too close to anyone that early in her life. She was paranoid about her own brother, I think she'd have probably looked at most flirtations or overtures as possible political gambits. Also, once it became clear that she was going to the Tower for more than just traditional teaching, they'd have put a hold on any plans for matchmaking. Even with her ta'veren-inspired feelings for Rand, and peer-approval, she is still obsessed with the propriety of the relationship. How far would she go against that training for a guy the Pattern isn't pushing her at? So it's entirely possible that she got that far without any physical interactions, IMO.

At the very least, she'd have a much better idea of how to get to first base in Tear, if she'd been there before. BTW, I'm pretty sure that if Gawyn had much experience before Egwene, it was in Tar Valon. Similar issues with Elayne, plus having to hang around and practice guarding her all the time. Of course, Gawyn being Gawyn, it's a good thing electricity hadn't been discovered yet, or he'd have practiced by frenching wall sockets.

As far as Lini wanting Faile to ditch Perrin, the time to put that plan into play is AFTER he rescues her. Not at a point when he's her only lifeline, and is the sine qua non of their group's cohesion and thus survival.