Are Moogles and Gaelikitten both connected to Azysla? (+theory?)

[Fenral]

Another thing Fenral, moogles were not at the servitude of Nighood, was his brood brother ( sorry the name is hard to remember )

Correct, they currently serve Hraesvelgr. He's the only one with his head still screwed on straight, so that's not really a surprise. In the past, though, during Zenith's heyday, it's not unreasonable to assume they served all three of them in some capacity.

Unfortunately, pretty much all we have to go on is 1000+ years of Moogles playing telephone, and who knows how much of that was lost or misremembered when one young mogprentice started dozing off for lack of kupo nuts.