Egwene was stated to be 17 in EotW, which was in the spring of the year 998. "The Dragon Reborn" was roughly a year later, in the spring of the 999. Tarmon Gaidon took place in the year 1000. The year changed at the end of "Lord of Chaos", the day Perrin set out to rescue Rand from the Tower sisters, so Dumai's Wells and beyond took place in the year 1000 NE. Egwene was therefore 19 at Tarmon Gaidon.

My rebuttal to the argument that Egwene is dealing with teenage hormones and emotional issues is that she should be actively scheming to get power. Recognition of the immaturity and biological setbacks teenagers deal with is exactly why we don't let people vote until they are 18, drink until they are 21 or run for office until older still, at least in the country where WoT was written. If Egwene can't help herself due to her age, she should sit back, shut up and let the people who have themselves under control, with centuries of experience at mastering those issues, run the show. Or maybe resign. Elayne is the same age, but she actually manages to function with high degrees of rationality and humility, and fights pregnancy hormones better than Egwene deals with teenage rebelliousness.

As far as the Padan Fain thing, I was saving that until I am done with this project, to write up as a full theory, but yeah, I totally agree. I think Fain corrupted her in the dungeons of Fal Dara as he claims later to have done to Pedron Niall and Elaida. It's the only explanation for her complete and total lack of faith or trust in Rand. I have noted many incidents where she shows an extraordinary lack of faith in his judgment or morality or self-restraint, in spite of his rather successful track record, or the approval of people such as Moiraine, or the trust of Nynaeve, who has extended close observation of him. It goes to a practically irrational extreme, to the point that only an effect as Fain himself describes his imposing on Elaida can account for it.