8 - Charitable Missions: Influence boosts from Gold gifts to City-States are increased by 30%.
You tend to be broke if you do shrines and temples, which you probably did if you are this deep into piety, so this is less useful than it seems. It is a big boost though. Religion is a good plan for a diplomatic win as it lowers influence decay, so specializing here and piling on Patronage is a good strategy.
7 - Evangelism: Missionaries' Spread Religion action erodes existing pressure from other religions.
A lot better than it looks. Lets you punch out a fraction of their religion before spreading. Night and day difference for a latecoming religion like byzantine. Early on, it is nearly useless, but once all cities are deeply seeded, you get to smile as you flip a contested city in one spread and they burn 3 spreads to get inferior results. The only trouble with it is that founder beliefs aren't that great, so getting a larger chunk of the world to be your religion isn't that great. Still, this lets you share religion with key civs for an ally/peace, 25% tourism for a culture VC, fulfill CS quests with missionaries instead of prophets, and more, so it's very good.
3 - Heathen Conversion: Missionaries convert adjacent barbarians to this civilization.
A faith based way to combat rebellion from being -10 happy and a new archer farming barb camp sort of tactic. Decent for a warmonger who is frequently razing cities. But if you are holding at -10 happy enough to get more than a wave or three of rebels, you have bigger problems. In the later eras, missionaries are rather expensive for solely this purpose, great people are better, but if you took say -30% cost on missionaries, this can be fairly nice for supplementing an army even late in the game. It is a problem of timing. In medieval/renaissance when you would take this belief, there aren't many or any barb camps left. A risky, questionable pick, considering the great alternatives, such as:
10 - Jesuit Education: May build Universities, Public Schools, and Research Labs with Faith.
This is a monster scientifically just to have everything right away, especially in production poor cities. There is enough to build already, and this unclogs a lot of the renaissance/industrial issues of too much to build, right on time. Resolves the "I need a workshop and university yesterday" debate, AND the factory/public school debate. A peaceful builder types wet dream, since you can branch out and try less essential wonders and buildings. And great for warmongering too, since you'll have high tech units and free up hammers to build them with, too. It also solves the problem of avoiding expensive forced great prophet pops in the renaissance. Just plain great.
2 - Religious Fervor: Use Faith to purchase Industrial Era (and later) land units.
Edit: Just tried it. They are wayyy too expensive. But it is versatile. In war, being able to restore your front line and pile on may make the difference between a costly stalemate or a decisive victory. In a pinch, like a backstab, more rush defense is always great. Buy walls with money, units with faith. But if you can go without in a war, and should you scout and use diplomatic resources instead, great people are a significantly better way to spend your faith. Having access to this alternative is nice, though there are better options, to be sure.
5 - Sacred Sites: All buildings purchased with Faith provide 2 Tourism each.
Situational. If you got 2 buildings for a follower, this is pretty darn good, but good luck enhancing into a second faith building, the AI loves them. Religion, warmonger, wide all go together, which makes this a non-bo combo with a peaceful cultural VC that is usually tall. It is a lot of tourism, however, which can support a rogue autocrat bent on world domination... muhaha... sorry. Seriously though, getting to exotic or familiar culture class with a powerhouse culture civ can buy you a few more dozen turns where you are happy and conquering, delaying the revolution just long enough for you to win a domination VC (or at least kill the offending oppressive ideology with fire).
9 - The Glory of God: Use Faith to purchase any type of Great Person starting in Industrial Era.
Absolutely fantastic. In my last byzantine game I bought 18 great people with this belief, 3 artists, 3 musicians, 4 writers, 4 great scientists, 3 great engineers, and a great merchant (needed fast money). Versatile & powerful. The wider you go, the better this is, temple spam giving access to great engineers without full tradition, great scientists without full rationalism, and making up for slow cultural GP production to boot, meaning you are free to cherry pick the best of the best policies or just the most relevant from each tree, which is quite powerful. You can do things such as Rationalism just down to secularism(specialist) & free thought(uni+TPsci), commerce just down to mercantilism(25% discount), Tradition just down to aristocracy (happy by pop, 15%wonder), Exploration just to Naval Tradition(+happynavybuilding) & Maritime Infrastructure (+3hammers coastal)
2 - Underground Sect: Your spies exert religious pressure on the cities they occupy.
Bleh. Although I'm not sure how much pressure it adds because I've never taken it. If it is less than 30-50, it's questionable. Tech stealing is more important than religious spread, and spies tend to go to holy city capitals, where this is useless.
5 - Unity of the Prophets: Inquisitors and Prophets reduce this religion's presence by half (instead of eliminating it).
A great way to eliminate someone's religion peacefully if you have open borders, send in a great prophet with a wave of missionaries behind. Knock out the religion with the great prophet, and seed it with tons of missionary pressure while it's empty. Repeat for all cities. If you are fast enough, with this belief, inquisitors won't save them. If they have high FPT, hold your religious army until industrial/modern, then get em with it; then they won't be able to afford inquisitors and if they settled their cheap prophets, you'll have them. With this reformation, high FPT, and a tactical spread, a worldwide religion isn't just a dream realized by the religious civs anymore (although it is of dubious worth because the founder beliefs aren't that great, but it's still really fun).