Kayla can't mean "crown of laurels" in Hebrew as Atarah means "crown" and they're clealy not anything alike.
Likewise, 'Aziz means "beloved" in Arabic, not Kaylin.
The thing about names like Kayla and Kaylin is that they're trendy, and many, many name sites make themselves appealing to big audiences by giving trendy names with fairly boring meanings, like Kayley and its variants, nice, interesting or appealing meanings. BtN doesn't do that, as I'm sure you've seen, so yes, all of those names can be traced back to the Irish Gaelic Kayley.
As for Katherine - I haven't had a chance to delve into the etymology myself, but I trust the judgement of Mike C (site creator) when it comes to controversial meanings. Chances are, he's right.