Getting back to the first song, Ayna Zorga, it comes from the Maghrebi Jewish repertoire, and has been recorded by Salim (Simon) Halali of Algeria and Simon Amiel of Tunisia in the 1950s. I believe it was also sung by Pinhas Cohen in Israel. You can find all of those singers’ versions in YouTube. (I just did) under a variety of spellings. in English and in Arabic, because of the different dialects.

Some tips about Arabic spelling and pronunciation:
3ayn“ = “eye”
“zarqa” = blue.
“Al-3ayn al-zarqa” = the blue eye(s)
“Al-3ayna al-zarqa” = her blue eye(s)

“3” is the Arabic letter non-Arabs can’t pronounce that sounds like you’re choking.
The “l” in the article “al” is pronounced like a “z“ before words beginning with “z.”
In North African dialects the letter “q” is pronounced like a “g” so “Al3ayna azZorga”