First confirmation is the block that our transaction is included in right?
Yes.
then what about the second confirmation and the next ones who is doing what to be considered the second confirmation?
Every block that is added to the chain after the block that has your transaction is another confirmation.
Why do miners have the freedom to select between transactions?
Because that was the only way Satoshi Nakamoto could think of for the system to work.
Why can't full nodes do the confirming and miners only mine new bitcoins?
Adding transactions to the blockchain and extending the blockchain with a proof-of-work is what makes bitcoin work as a decentralized cryptocurrency, but doing that costs money and effort. Therefore, t make sure people would do it, an incentive structure was built in to the system. Whoever successfully adds a block to the blockchain gets to keep all the transaction fees.
In the beginning there weren't many transactions yet. Also, bitcoins weren't worth any money yet. Also the system needed a fair way to distribute the almost 21 million bitcoins that the system would have. So, the bitcoin system allows each block that is added to the blockchain to include a subsidy of new value. That subsidy starts at a value of 50 BTC, and is cut in half every 210,000 blocks. The idea is that as bitcoin gains popularity, the total value of the fees paid per block will increase (either due increased exchange rate, increased number of transactions, and/or increased fee per transaction), so less subsidy will be needed later to provide the incentive.
This is what mining is.
