I can answer a couple of the guild questions definitely, and make suggestions for a couple more.

The Explorers Guild increases your movement points. I now have two of these, and it's noticable the difference it makes. I can't say for certain if the increase is just within a certain map distance of the guild hall, just within your borders, or globally. I don't have a Master Explorer's Guild yet, so also not sure what benefits will come from the higher level build.

I got a Theologians Guild last night. It increased piety of priest trained there by +1. I expect each level will add another +1.

As to triggers, I think the Explorers guild trigger was getting map info around the world. I've sent a number of diplomats, spies, and ships out travelling the map. I got the Theologians guild after a spate of heavy priest/temple building. Others are less obvious.