Amathera worked in Nynaeve and Elayne's inn for a short time until the chaos in the city died down, and she could rally her loyalists to place her back on her throne. Elayne wanted her to get a taste of life among the proletarians before she went back to living high on the hog. This would have constituted an excess of time necessary for a WoT relationship to begin. Trakands develop deep feelings for people who never speak a personal word directly to them, so a couple days of hitting on her as she serves him wine is plenty of time Juilin to fall head over heels.

Egeanin "found" Bayle when he recognized her in Nynaeve & Elayne's company and captured her. They sailed from Tanchico on his ship to ditch the male a'dam, and got boarded by a Seanchan vessel. In order to save her ass, Egeanin handed over the male a'dam, thinking Rand would have been forewarned and not have to fear it. Domon behaved inappropriately during this incident by Seanchan standards and was enslaved, and Egeanin bought him. His ship was presumably seized and his crew either hired on with the Seanchan or got new jobs. "Firefly" not withstanding, ship crews are pretty much NOT families, and men come and go from one crew to another, the same way any other employee in a high turnover profession might. The Seal Domon had was confiscatd by Egeanin when she captured him in tGH and handed over to High Lord Turak. It is one of the two broken ones Moiraine shows Rand after Falme (the other being from Turak's own collection from Seanchan). The other artifacts would presumably have been lost. He was no longer confined to one ship by the time Nynaeve & co re-encountered him in Tanchico, so it is anyone's guess where he had them, or what would have happened to the ships and anything else he owned once he was enslaved. Aside from the possible male angreal, I doubt any of it would have been much use in the story.

I would assume Paitr left because being called a "Darkfriend" in public tends to make one unwelcome. It is suggested that he simply went where his cell was assigned, since he was still under the authority of the people who commanded him in Andor. The hometown of the CoL would be someplace that the Shadow would definitely want operatives in place. Shiane also has been bouncing around on missions, being sent to approach Rand, assist Carridin and then do whatever she was supposed to with Elayne in Caemlyn.