Was Herodotus alive during the Persian Wars?

No -- well, mostly not. Herodotus was an infant during the end of the Persian Wars. He compiled reports (of mixed and sometimes dubious veracity) from various persons to whom he spoke in his travels, and may have drawn on earlier historians whose works are now lost.

Herodotus is the earliest remaining Greek historian; no contemporary historians of the period (and bear in mind that history as a discipline was essentially invented by Herodotus and his successor Thucydides) left works which survive. I believe Aeschylus' tragedy "The Persians" is the only primary source, by your definition -- which doesn't really make sense, by the way -- remaining to us, other than inscriptions. Aeschylus fought at Marathon and The Persians depicts the Battle of Salamis.

Herodotus Persian Wars

Herodotus was not alive during the Persian Wars. He travelled extensively, and spoke to many people to gain information, but generally he never named his sources.

Yeah he was and yeah it would be!