In the episode where they found out Ari name they berkata 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 tahi lalat 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 NCIS fandom page: "Ari Haswari was born in 1969 to Dr. Benjamin Weinstein (the undercover alias of Mossad agent and future Mossad director Eli David)".