Ok, so the actions I'd like to perform:
1. Gather the miracle fern. This should not cost influence, if I'm understanding it correctly?
2. Encourage the people to work harder for the betterment of themselves and others.
3. Encourage the people to try to capture and tame some of the Fae Death, for their...milk, I guess.
Not using the third influence right now because I can't think of anything.
1. Yep you can do that.
2. You should be more specific about the outcome your hoping for.
3. Let me explain why this is a terrible terrible idea (also you can't do it do to population restrictions) they are the size of mice, so the milk you'll get from one is minuscule in order to get enough for a single unit of milk you'd need like 1000 of them, also they have claws that when they cut you, you die within minutes, like foam at the mouth eyes bleeding death, their milk isn't worth it.
Is there any advantage for Akethoria to pursue total control of the sea? Also, can influence be used to create a religion?
You mean besides having total control of the ocean?
Yes, religion is a great way to have influence, also building a church rewards a hero slot (for preacher/prophets/popes/etc, but hey)
Simply being the leader of a church gives you influence over anyone (even other nations populations) who worship it.
To start a religion you need to build a temple which is like 3 wood (or stone) Churches provide happiness to the population so it's worth building foreign churches even if you don't control the religion.
If your a ruler you can also be the ruler of a religion, but hero's can do the same too.