That was an amazing technical improvadvancement and symbolizes a historic milestone in history.

While improvement is not "wrong", I think advancement is a more common way to talk about progress with technology.

Besides the Moon, Mars, however, Mars has come to us recently.

My correction makes this more grammatically correct. However, to be more nuanced - as written, this sentence implies the Moon has come to us, versus us going to the Moon. Perhaps you could say: Besides the Moon, however, Mars has become within our reach recently.

Elon Musk, the richest and one of the most talented guys on this planet, has expressed many times in different scenarios, willingness to send regular travelers to Mars.

I firmly believe I will witness theis memorable moment before I pass away.

Your text is not grammatically incorrect, but using "this" puts more emphasis on the memorable moment.

That was an amazing technical improachievement and symbolizes a historic milestone in history.

“Historic” and “history” seem redundant here.

BesidesIn addition to the Mmoon, Mars, however, has come to usas also come to our attention recently.

Elon Musk, the richest and one of the most talented guys on this planet, has expressed many times in differenthis desire to scenarios, willing to send regular travelers to Mard passengers to Mars a number of times.

I believe I amwould be unable to afford the travel fees, but I willould feel excited if someone rich canould fly to Mars as a tourist.

I firmly believe I will witness theis memorable moment before I pass awaywithin my lifetime.

We prefer “within my lifetime” for an optimistic tone. To write “before I pass away” ends the writing with a subtly sad tone.