Is it possible to mine just for the fees?
Consider this as well: once all the 21 million bitcoins are distributed, there won't be any coinbase in the new blocks and at that point, the miners will indeed be mining
only for the fees.
I am beginning to understand it. So during mining the transactions will be piling up then when a block is found the pool operator decides to add to the block.
OK, I am going to start my own pool. Which is the best pool software?
It's not about "deciding" to add a block. If you're mining, you are in a race with many other people to "add a block". This answer has more detail:
The transaction fees are calculated by the pool when they decide to add the transactions into a block they are trying to mine. The fees are not specified by a number tagged on to a transaction. It is actually the difference between the inputs and outputs, the unused amount of the inputs.
So the fees are in there when you find a block. As the mining computer (or pool), you get to keep the difference between inputs and outputs in the transactions which are in the block. You
can make decisions about which transactions to try to include in the block as you go looking for a block and receiving transaction broadcasts on the network.
About starting your own pool, you're going to be in tough competition. Since you're just learning the very basics here right now, it's doubtful that you're ready to compete with the big players out there. But nice enthusiasm tho!