As to the origin of the Skeksis, The Dark Cyrstal and Dark Crystal: Age of Resistance seem to agree. In episode 7, the Heretic and Urgoh put on a puppet show explaining the origin of the Skeksis and Mystics, and it's essentially the same: that the Skeksis and Mystics were once one as the UrSkeks, and they need to be re-joined.
As for the Skeksis that appear in Age of Resistance, it's been established canon from The Dark Crystal: Creation Myths, that there were originally 18 UrSkeks that came to Thra, but 8 ended up dying before The Dark Crystal, with two being killed very soon after the Great Division. (Though as many as 21 different Skeksis names have been listed in the various media.) So if Age of Resistance is closely following the established canon (though already there is evidence of some deviation), we can expect to see at most 16 Skeksis. Some Skeksis that appeared in The Dark Crystal have not appeared in Age of Resistance, as of the first season, but are definitely around somewhere, as they are mentioned in dialog in episode 10, along with skekLi the Satirist and skekSa the Mariner who only have appeared in the graphic novels.
Those that appear in both The Dark Crystal and Age of Resistance:
- skekso the Emperor
- skekSil the Chamberlain
- skekZok the Ritual Master
- skekTek the Scientist
- skekAyuk the Gourmand
- skekEkt the Ornamentalist
- skekOk the Scroll Keeper
The following Skeksis appear in Age of Resistance but not The Dark Crystal, though most or all were previously named in some of the various other media:
- skekVar the General
- skekLach the Collector
- skekMal the Hunter
- skekGra the Conqueror / the Heretic
Those that appear only in The Dark Crystal:
- skekUng the Garthim Master
- skekNa the Slave Master
- skekShod the Treasurer