It’s probably difficult for some folks to wrap their heads around Vader being the Dark Lord of the Sith whilst being subservient to a non-Sith Palpatine because since 1999, the Sith have been portrayed as apex predators who have a monopoly on dark side mastery. But this is purely an invention of the prequels.
You do realize that the fact that Vader calls Palpatine his master obviously means Palpatine was a Sith in TESB and ROTJ? Like yeah you can rationalize a different explanation but it’s clear that’s the intention. There’s no need to jump through hoops for another explanation. The scripts for all three call Vader a Dark Lord of the Sith and the Emperor is his master.
Eh, I don’t think it’s as open-and-shut as you’re suggesting. The early conception of the Sith leaned more into the warrior aspect, which Palpatine, as a sorcerer, lacked completely. All that’s implied in the OT is that Vader the Sith swore fealty to the Emperor, who’s powerful in the Dark Side, but seems dismissive of lightsabers.