For the Talmid Family Tree, it's actually on this wiki. User_blog:FleetCaptainT/The_Talmid_Family_Tree_2!! As for that page on that wiki, it's unfinished (obviously). xP
Fleet Captain Talmid is here!!! By revealing his name, I did intend for you to realize that this is not the same Fleet Captain Talmid that we know from Talmid Show, but a counterpart from another dimension who is mostly the same, but already carries a different first name.
Spectre Borg are unfortunately not my original creation, a former LEGO.com user known as Star-Hunter on the Creation Lab introduced them as part of the PCG roleplay story, "Operation Omega," where they fight off the Spectre Borg. I wrote a spinoff of sorts where the Spectres come back, and whatever's on the CL goes anyway, so I'm sure it's of no offense to use them here. So now Talmid and the Borg are in LU. Exciting, indeed...
For the people Edwin is talking about, Star Trek frequently has powerful and omniscient-like beings (such as the Q, or the Prophets) show up, so he could just be referencing them, and not people specifically like Kate as in like Nexus Figures.
These are all powers Kate already had learned or trained in SOTS, although how she continued to practice them if at all after coming home is unfortunately lost from memory (RIP). So technically she's relearning them now, and they're coming easier this time since she already knows how to do them, but has just forgotten.