In the episode where they found out Ari name they сказал(-а) his father was Dr. Benjamin Weinstein so how did Eli David become to be known as Ari's father?

Ziva was only his half-sister, so Eli might just be his father in this sense, not in a biological sense.

Well we all know that Ari was born to be a моль in Hamas. Then if Hamas finds out that one of their agent's father is Mossad they would kill him and then Eli wouldn't have his mole...

I was wondering this myself; found the answer on the Морская полиция - Спецотдел fandom page: "Ari Haswari was born in 1969 to Dr. Benjamin Weinstein (the undercover alias of Mossad agent and future Mossad director Eli David)".