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I have a hard time understanding the meaning of below sentence:
"To confirm within 48 blocks, a transaction fee of 1 satoshi/byte is required."
I have 2 questions here:
1) Does this mean that the first confirmation of the transaction will probably happen within attachment of the next 48 blocks?
2) As soon as the first confirmation is received, is it guaranteed that this confirmation will increment with all future block attachment (which is every 10 mins)?
Not sure where you are quoting that statement from. Seems to be a promise on something that is probabilistic.
1.) From that statement yes the first confirmation with happen within 48 blocks.
In practice, it depends on the current mempool size (how many transactions are waiting to be confirmed) and the transaction fee (miners are incentivised to choose the transactions with the highest fee) relative to the other transactions in the mempool. I would not go as far as to say with fee of x you will receive a confirmation in y time because at the time of adding the transaction to the mempool you might see that your transaction should be in the mempool (due to your fee) but every 10 minutes there are a block load of new transaction that are added to the mempool with higher fees.
2.) Yes, after the first confirmation the next confirmations will tick at an average of 10 minutes each (slight correction from your statement, not every 10 minutes but rather 10 minutes on average).
To elaborate, if there is x hash power in the network AND the network sets the difficulty to find a block then probability dictates 1 block every 10 minutes. However, if there is additional computing power that joins the next then the time (on average) to find the next block will be <10 minutes... at least until the network readjusts the mining difficulty.
