The article and the lecture are about doubts concerning whether ancient Phoenicians circumnavigated Africa.

You could say "doubts surrounding" as well

The author believes that the Phoenicians could not have had a journeyed around Africa.

You can also say "traveled" or "gone on a voyage"

Firstly, the author claims that, even though they were skilled- sailors, their ships were not sufficiently prepared for long trips in the open ocean, due to the fact that ships were small and were made from wood.

On the other hand, the lecturer disagrees with that statement and declares that Phoenicians were surprisingly well -equipped.

Their ships were strengthened with metal panels and also, they were also repairing and maintaining their vessels for a very long period.

You could also say "a very long period of time"

Furthermore, an ancient civilization couldn’t have navigated Africa without any equipment and navigation tools.

I think it's best to specify where the navigation is taking place if you use the word "navigate" as a verb, in this case - Africa

However, even though the lecturer agrees with the complexity of the landscapes, he considers the fact that they were skilled sailors and they used stars and other natural landmarks to navigate in the open ocean.

In conclusion, according to the author’s last statement, there is not a single real historical evidence to prove ifthat Phoenicians ever circumnavigated Africa.

You could say "prove that" or "prove whether", I think that's a bit more common than "prove if"

All survived records indicate that they only werewere only interested in establishing trade routes and colonies.

But the lecturer challenges this and mentions an ancient Egyptian drawing that depicted the Phoenician’s ships passing along the coast in north Africa.