Do they have planes to rule like all the daedric princes?

Mundus (the realm where Nirn is) is the place they "rule", they sacrificed much of their power to create Mundus. There is also sovngarde, which is a realm of the nordic god, Shor. not sure what else though.

I thought fhey had some heavenly planes or something

There's their corpses/plane(t)s in the sky (like the moons for Lorkhan). Not sure what they're like though. I do remember something about expeditions to them in spaceships though.

spaceships?.....I gotta read up on lore more often.

Sovenguard, the planets, and Mundus are their planes.

They way I view it, the Mundus is a conjunction of the eight planes into one, however, they do not posses a military totalitarian system like the Daedra.

That was to Aetherius, expeditions by the Sunbirds of Alinor and Reman's Imperial Mananauts.

The Eight Divines connect Mundus and Aetherius, so even though the Divines are in Aetherius, they also have the "planets" as their planes. In truth they are just that, infinite planes, and not truly planets.

People have been to the plane(t)s, though. There's an Orrery somewhere that's said to have its planets made of "authentic celestial material" or some such. How exactly they got there, though, who knows. Maybe space/voidships, maybe teleportation, maybe dragons.

Yes.

Not corpses. The Aedra are still alive, although they (unlike daedra) CAN die (they just come back after.) The only Et'Ada to have truly "died" is Lorkhan, and even though his soul doesn't come back as him again (as it does the other gods) it still is continually recycled through mortal bodies.

Also, there has been a long history of extranirnian (and extra mundial) travel on Sunbirds, via teleportation, and in ships.