They seem to be accurate from what I can see.
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.
:-)