So when mining we actually calculating other people transactions.
No, mining actually perform lots of SHA-256d operation of block header.
The whole point of bitcoin is that it has no fees if you use professional mode wont that defeat the purpose of not having a central computer?
I don't why you make such assumption. But TX with 0 fee was thing in the past when miner simply use default behavior of Bitcoin-Qt rather than maximizing profit.
This is absolutely true and logical. My question is about the possibility that Bitcoin will not be available to everyone due to the scarcity factor that will affect the supply in the market and the difficulty of making transactions due to the high transaction fees after the completion of mining the last Bitcoin. Can't we talk about the "death of Bitcoin" clinically as happens with humans? I read articles about these futuristic approaches and I find them really interesting because they pose the issues from a completely objective point of view. What do you think?
There will be solutions for this, technically and unit of bitcoin. With the expectation that Bitcoin value will grow up and price will increase more, 1 satoshi will have more value in $ with time, and new smaller units can be created and use for Bitcoin transaction fees.
Solutions like Lightning Network, Bitcoin side chains and something new can help Bitcoin technically.
Sidechain Observer - Bitcoin L2 Projects & current state of development[Did you know?] Bitcoin Table of UnitsHard fork to allow smaller unit on Bitcoin network is also option.