Does Higher Rifts Give Better Loot?

Greater Rift Guardians drop the best quality loot in the game, and players moving into higher Grifts ("higher" varies between patches and continually increases due to power creep) will generally see 3-6 legendary items per Guardian, plus stacks of materials and gold.

Do greater rifts drop better loot?

You get more drops, but the quality stays the same (loot is random). And no, there's no cap. On a GR100 you will get a few more legendaries on average than on GR80.

Does rift level affect loot?

Monsters killed in Greater Rifts don't drop any loot. All the Gold-generating effects (such as Boon of the Hoarder or Goldskin) are also disabled.