B4

How long has man been on earth? Let us travel 5,000 years into the past. We are in the days before man learned to write. Recorded history hasn’t begun / has not begun yet.
(present perfect, т.к. мы перемещаемся в прошлое. Также перемещается и точка отсчета. Мы в 3000 году до нашей эры и запись истории еще не началась)

NOT BEGIN

B5

Yet there are people, about five million of them, living on all five continents.

(Participle I, “живущие”, подходит по смысловому контексту)

 LIVE

B6

The earliest true human being, Homo sapiens, appeared in Europe more than 50,000 years ago.
(степень сравнения)

 EARLY

B7

Daedalus was a brilliant architect and inventor of  ancient Greece. He was so brilliant that King Minos of Grete kept him as a prisoner.
(past simple, т.к. действие произошло тогда, в прошлом)

 KEEP

B8

The King didn't want / did not want to let him go back to his home in Athens.
(past simple, т.к. действие произошло в определённое время, в прошлом)

NOT WANT

B9

Daedalus lived with his son Icarus in a tower of the palace, and King Minos made him invent weapons of war that would make his army and navy even more powerful than they already were.
(степень сравнения)

 POWERFUL

B10

Although Daedalus and Icarus had every comfort, they longed to return home to Athens. Daedalus looked at the sea, and he realised that even if they managed to slip out of the tower and find a little boat, they world not be able to sail far. One of King Minos's seamen would spot and catch them very soon.
(seaman – ед.ч. seamen – мн.ч. )

 SEAMAN