This is a good question, but needs to be addressed in parts:
What forms of currency are used in this world, and what is the purchasing power of them? For example, if the Ravencloaks are offering a reward of 50 gold for information about a missing princess, is 50 gold a lot of money? How much can 1 gold buy, in terms of food, lodgings, basic equipment, etc? Are there silver and bronze coins too, and if so what is the exchange rate?
The world operates on a "Gold/Silver/Copper" system. Silvers and coppers being the most common, rare being more reserved for expensive purchases. An amount of 50 gold is not a
lot of money, but it is also nothing to scoff at either. An amount of 50 gold could purchase you a decent horse, a good (but not magical) weapon, or could put you up in a very nice inn for a couple of months. It is "a fair bit".
(W)hat is the exchange rate? (The relative value of silver to gold by weight seems to stay consistent historically at around 100 to 1).
10 copper to 1 silver, 10 silver to 1 gold.
Do Khare and Tethis have different coinage with different heads of state stamped on them?
No. Neither city has a head of state and both are very much linked to each other in terms of trade that they run on the same currency systems.
Are there any other power centers where their currency is valued in many places as a reserve currency, for its stability and the military might of the king or emperor who issues it?
If there are other power centers, these are not known to the characters at this time. As far as the currency is concerned, no.
A relevant note about money in the Outer Sanctum.
Money largely doesn't matter in a meaningful way.
If you're broke, you aren't going to starve and die on the street. If you're extremely rich, you still can't buy an armory full of magical weapons. Money is an RP tool, not a mechanical system in the Outer Sanctum.
To use a dungeons and dragons analogy, money doesn't tend to matter when characters "go buy rations" or "stay in an inn", but do matter when buying magical items worth several thousands of gold. Your
character should largely be dictating what their purchasing power looks like. If you are a slave, peasant, or farmer, you will probably not be staying in really posh places. Your descriptions and the decisions your character makes should reflect this. If you come from a wealthier family, dropping 20 gold for a round of drinks at the local pub might not be a big deal.
The point about the "value" of currency is similar to the value of many things in an RP—they are tools to tell a story, and as such, you have it when it makes sense and you don't have it when you shouldn't.