See my title. Why do people doubt the nice Cannoli?

Actually it was more like the way she kept getting annoyed or conspicuously ignoring Elayne's & Min's obvious interest in him.

Yes


Figured it was Elayne/Berelain. Didn't realize Elayne prioritizing Tower over Rand. She wasn't really, but she did say her mission takes priority and she wasn't going to forego being Aes Sedai for him. True, she is trying to work the system from within in his favor, but she was still saying even as Egwene was signing over Rand's pink slip, that he was going to have to settle for the Tower's sloppy seconds.

That was Egwene and Aviendha doing their punishment laps after the sauna in Rhuidean. Egwene pays lips service to the notion that she only wants Rand to be with Elayne if he wants it too, even as her thoughts give her the lie. Which pretty much shows her priority - either she was only making the expected token gesture towards pretending to care about Rand's happiness too, or else she wanted Rand to love Elayne because Elayne would not be happy if Rand was forced to be with her.

Mat and Melindhra. She is disgusted with them and specifically cites their age difference, placing it at about ten years - two books before she will send Land who has twice as many years on Nynaeve after her.

Only a little, and only because Nynaeve is criticizing him. Since he was not in the room to receive the thought-praise, setting down Nynaeve mentally was an easy choice. You can see when they are both in the room how she grapples with whom she should turn on - Mat or Nynaeve, Mat or Nynaeve, such a difficult choice. I think the deciding factor that made her remonstrate with Mat, was that she could get some shots in at Rand too. Once he was gone, and Nynaeve is criticizing him, she can safely turn on Nynaeve without supporting Mat. Hence her scoffing at Nynaeve's criticism of Mat's promiscuity.

The jury is still out on that one. There is no direct evidence, and one can support Myrelle's "So that's why..." when Egwene reveals their relationship, as an indicator that he refused Myrelle. Or it could just be that she could tell he wasn't liking it. Anyway, nothing references Lan until Book 7.

Reference to sending Lan after Nynaeve without consulting him, despite his frequent claim that nothing could happen between them, what with him being all deadly. Egwene is the teenage authority who thinks she knows better than them.

Nope. That was Siuan in New Spring. They were trying to get close to one of the potential Dragon baby-mommas who was in seclusion, and Siuan was macking on her servant who offered to get her a job with his mistress. The way she phrased it was ambiguous, and Moiraine took it to mean that he was asking her to sleep with him. Siuan says that is not the case, but says if it had been that would not have been a big deal.

Always

Hah! Good one.

And mentally working her way around the Two Rivers custom that she is supposed to get permission from her mother about giving away milk before the deal for the cow is finalized. She's thinking "Oh, Mom trusts me. I'm sure she'd say yes even if she never met Gawyn!"

That was during her T'A'R meeting with Aviendha in CoT, when Aviendha is laughing about Elayne's pregnancy troubles, but is plainly happy for her and excited about the pregnancy, and Egwene thinks that "...Aiel ways were peculiar, to say the least." Yeah, why be happy for a friend who has something good happen? It doesn't bring you power or status, after all!