Yeah a lot of stuff in Deep Space 9 is setup throughout The Next Generation, in a way it's a spin-off of TNG. Lwaxana Troi is the mother of one of the main characters on TNG, for example. (random fact: the actor is also the widow of the creator of Star Trek, Gene Roddenberry). She also acted on the original series, but played a different character.

There is definitely a religious slant throughout the show, especially when it comes to the Bajorans or Sisko, but generally doesn't act as a deus ex machina plot device. Okay I can think of one plot point of the top of my head where it's a bit deus ex machina, but it's still very enjoyable and arguably makes sense within the context of the entirety of the show. Overall I'd say the Bajoran / wormhole alien religion plays an important part in the show, but more for setting / theme and less for major plot points, and in episodes where it is a plot construct it is well done and makes sense in-universe, unlike some other shows I can think of (like Battlestar Galactica).

Have you been introduced to the Cardassian named Garak yet? In my humble opinion Garak (and Gul Dukat, whom you've already met) are some of the best characters ever written for TV. The character development over the seasons is organically great, for most of the characters, really.

There is an overall main story spread out throughout the show, which I think doesn't really kick into full gear until season 4 I think? Deep Space 9 is different from the other Star Trek shows in that the other shows generally don't have an overarching story, each episode is more or less self-contained, which made DS9 quite the radical contrast at the time it was released.