The zajal links you posted are actually not bad at all Mount_Amel, never really heard anything for Talee3 7amdan....but I just found out he's pretty good
However, when you wanna hear real Lebanese zajal

, you should go for the true satrs, like "Moussa Zgheib" and "Zaghloul Damour" and "Khalil Roukoz" !!
This
link for example contains a fair amount of downloadable zajal music for Moussa Zgheib (some call him Moussi with an "i" as well )
And an amazing zajal extract written by Moussa Zgheib, sung by Najwa karam
Mouwwel aL Adyan
And here is a prodigious
list, of lebanese zajal text....with this database, you could impress your audience pretty well, since zajal is a custom nowadays, where the audience can participate by replying with the ending
As for the origins, I'm pretty sure it's Lebanese

Lebanese Zajal is as old as Amir Fakhreddine, and even documented to be older (1200-1300). But in only became popular as we know it today (ya3ni competition, w tawli w mezza w khass w tabbouli, w dirbakki

) in the thirties, with "Cha7rour l Wadi" and others....
There is a possibility that the palestinians discovered their own zajal as well......but as we arabs tend to do sometimes, is try to improve our methods by comparing to others.

I will try to provide more details during the upcoming days.