Price of a Coin.
1. The profitability algorithm the owners of the pool designed to compute the price to advertise to the miners the value of the coin, taking into account things like orphan rates, stales, network difficulty and availability of exchanges and the prices on those exchanges.
Profitability.
1. As Einstein would say..."It's all relative" If you had 1 bitcoin, and the price of bitcoin doubled....you still have 1 bitcoin, but now its worth twice as much. Has your mining returns doubled? No you are likely still earning the same amount of coin per day. So while the number of coins or ratio of coins per hash likely won't change, the value of the worth of the $ of the coins would increase, so is that doubled returns $ wise or coin wise?
If one day BTC is worth $50, you make $50 and get 1 coin. The next day it's worth $100, you make $100 but you still only get 1 coin.
Some would see that as a double of earnings, others would see it as the same return on their mining but the return is just worth more today than yesterday.
2. I would have to say price the exchanges are willing to pay. If an exchange has a run on a coin and the price rises on that exchange the next time the data is transmitted to the pool the algorithm on the pool should compute a slightly higher profitability for that coin.
Difficulty
1. Based on the coins targeted block time and block reward determines how many of those coins are made per day.
2. The coin's difficulty and other factors are figured into making the pool's profitability.
3. So they can tell how many miner's hashrates they can stick on a coin before it becomes overloaded and not profitable to mine.
Which is why you will see top coins float up and seems like no one mines them and then the coins drop to the bottom of the list without ever seeing the radiant bar of pooled miners hitting the coin.
from:
https://en.wikipedia.org/wiki/Bitcoin
The "Dudes"
1. There is no single administrator,[7] the ledger is maintained by a network of equally privileged miners.[3]
2. There is no central server, bitcoin ledger is distributed.[105]
3. BTC is a bad example...as no one really knows WHO invented it. Other coins are all forks of bitcoin into sha-256 or other algorithms which then branched off into other coins and other algorithms. Typically the owners of a newly created coin keep some back for themselves so after the coin moons they can cash out. If its a new coin via a fork, then whoever had X coins before now has those same X coins plus the same X amount of the new coins from the fork. Do they have a say over it, it depends on the coin. Some coins allow the miners to vote with their hashing power on decisions, other coins implement what they want and feel will help their coin, usually via a committee or CORE group of developers. If the users/miners of a coin do not like the direction the devs are taking a coin they can ignore the changes, keep with the old version of the coin and invalidate the new design by enough sticking to the old design.
Hope that gives you some answers you can use.