There are actually four or five: missionaries (inexpensive weak offensive unit), apostles (expensive strong offensive unit with random unique bonuses), inquisitors (defensive unit), and gurus (support unit, heals adjacent units). There are also warrior monks, which only one religion may have and, despite being melee units rather than religious units, will spread their religion when defeating another unit in combat.

I'm still a little torn on the religious mechanics in 6, but it's certainly the most involved the series has ever made it, and probably strictly better than 5's implementation. Your points about AI trading are true to home, though there have been a few improvements to trade routes in patches and the recent expansion (by adding a "repeat route" button to the trader menu, and also generally by nerfing trade routes so you generally have fewer of them).