1. You might not have enough vice for robbing the congregation. I'm pretty sure you need to have unlocked stealing larger things for that.
3. The worshippers offer quite a few perks if you befriend them. There plenty of lore you can learn from them, and a few exclusive spells.
4. There is a book you can read that gives a skill to skip to two progress on your first read of a book.
The purple gems in the second area are intended to be more for people who want to RP Alicia gaining power than anything else. From the perspective of trying to win they are the last mental changes you would want to take. The fusions in Riverflow are odd. They used to be better, but were adjusted or balance once or twice. They are balanced around paying extra to get more out of one infusion.
Admiral Ramirez the duels were the job. There is a second (underground) bar that you can work at to earn money and trust with the worshippers. The second bar also has a chain of lewd scenes and grants access to one method to progress a quest.