OK, changing complexity based on available hashing power makes sense ... but gives me a couple of other questions
It seems like the number of transactions and miner compensation would also effect the coin creation rate
Any altcoin can manage these things however they like. So you'd have to investigate each altcoin you might consider separately.
However, transaction count and miner compensation has no effect at all on coin creation rate for Bitcoin. The protocol manages the difficulty to keep the block rate near an average of 1 per 10 minutes, and the number of new coins per block is permanently set: Starting at 50BTC per block for the first 210000 blocks, and then cutting in half (rounding down to the nearest 0.00000001 BTC) every 210000 blocks (approximately every 4 years or so).
I haven't studied the compensation system yet, so some of this may be erroneous.
For Bitcoin, it is erroneous, but you're new to the concepts so it is expected that some of your assumptions might not be entirely accurate. Ask questions here, and you'll learn quickly.
If i understand correctly the only way bitcoins are created is as compensation for miners completing the verification. Is that correct?
Effectively, yes. More specifically, each new block of transactions added to the blockchain with a valid proof-of-work is allowed to assign a specific maximum amount of new bitcoin value to a set of one or more transaction outputs. That maximum amount is currently 12.5 BTC, and is cut in half every 210000 blocks (approximately every 4 years or so).
Since the solo-miner (or mining pool operator) is responsible for "completing the verification" by building the blocks of transactions, they are in charge of where to assign that new value. The intelligent thing to do (that most miners do) is to assign that new value to one's self (or to the participants in one's pool).
If some one wants to just buy a bit coin they have to buy from an existing owner?
Correct.
Verifying a transaction takes a number of independent verifications correct? 3 or 6 or some thing like that?
Incorrect.
Bitcoin has a concept of "confirmations". As soon as a transaction shows up on the network it is instantly "verified" by EVERY node, miner, and wallet on the network. Invalid transactions won't ever even show up beyond a few poor software implementations. At that point the transaction is valid, but UNCONFIRMED. This means that it isn't permanently stored in the blockchain yet.
At any time a replacement VALID transaction could show up and if the replacement transaction gets confirmed then the earlier replaced transaction instantly becomes invalid and is dropped from the network. For this reason, it is important for users of the bitcoin system to wait until their transaction has been included in a block of transactions in the blockchain. The first time the transaction shows up in a block in the blockchain, it is said to have 1 confirmation. Each additional block of transactions that get added to the chain on top of the block that contains the transaction in question is considered to be an additional "confirmation". The more confirmations a transaction has, the deeper in the blockchain it is buried and the more difficult and expensive it would be for someone to replace that block.
Generally, 1 confirmation is enough to feel pretty confident that the transaction will not be replaced. Depending on how risk averse you are (and the value of the transaction), you might feel more comfortable waiting for a few more confirmations (just to be sure). By the time you get to 3 confirmations, the transaction will almost certainly be permanent unless there is a significant event in the Bitcoin ecosystem that has resulted in a sustained fork of the chain. This has only happened a few times in the history of Bitcoin.
How much compensation is paid?
A solo-miner is allowed to assign 12.5 new bitcoins PLUS the sum of all the transaction fees of all the transactions that they included in their block. Participants in a mining pool typically receive a percentage of that reward that is based on the percentage of the pools total hashpower that the participant provided. Each pool has their own rules about how they distribute the earnings, and what fees are withheld for the pool operator. You'll need to investigate the specifics of any pool you choose.
Is it a flat fee per transaction verification or does it depend of the value of the transaction?
For solo-miners, it is a flat 12.5 BTC
PLUS the sum of the transaction fees of all the transactions included in the block that the miner built and solved. For pool mining, it is pool specific, and you'll need to investigate the policy of the pool you choose.
This creates an increasing cascade of coin creation. If one transaction creates compensation for 6 miners (or pools) then that creates 6 more transactions to verify each of which creates more compensation.
Incorrect. The miner (or pool) builds a block of as many transactions as they can fit within the current blocksize limit. Included in that list of transactions is the transaction that pays the miner (or pool). So that transaction is immediately "confirmed" when the solved block is broadcast. A block (and all the transactions in the block) only creates compensation for 1 solo-miner (or mining pool).
Without the cascade, coin creation would be dependent on transactions (not just hashing power) for new coin creation. If no one created transactions no new coins would be created.
Bitcoin blocks are created and solved on average once every 10 minutes. If there are unconfirmed transactions waiting to be confirmed, then they can be included in the block (up to the block size limit). If there are not any unconfirmed transactions waiting to be confirmed, then the miner (or pool) still builds a block that includes the 1 transaction that pays themselves the 12.5 BTC block subsidy.
... This can't be right ... I must have this wrong.
Don't worry about it. Keep asking, and reading. You'll get there. This stuff isn't intuitive, and you'll need to escape many incorrect assumptions that you've probably already made about how this all works. However, once you've got it all straight in your head you'll find that it's all pretty elegant the way it fits together.
