Both are pretty rare now, but Danielle is the more common spelling. It also matches the way the -elle is used as a suffix in many diminutives (e.g., cervelle, ruelle, passerelle)
-elle is pretty clearly descended from one of the usual Latin diminutives (also visible in e.g. Spanish tortilla). -ette seems to come from a much rarer one?
There's a fun map on Spanish wikipedia of which diminutive forms are preferred in which parts of Spain: https://es.wikipedia.org/wiki/Archivo:Diminutivos_del_espa%C...
Yes, both are used commonly. In names, there are Isabelle, Gabrielle, Cyrielle, Annabelle, Axelle, and many others. I am not sure there is any rule.
https://en.wikipedia.org/wiki/Gabrielle_(given_name)
Another commenter believes, in Romance languages, that the "-a" feminine gendered suffix is diminutive compared to "-o" masculine or neuter suffixes, but that is not true. Not for Latin, or Spanish or Italian or even Greek.
(1) El isn't a name for God in Hebrew; it's just the ordinary word for any god. Like "god" in English. Conceptually close to ba'al, the ordinary word "lord".
The best-documented confusion of this kind that I know of is the Greek "Adonis" - in Greek, Adonis is a name, but even at the time it was recognized as being a Semitic loan from a word meaning "lord". We know enough about the cult of Adonis that we can identify him with a specific Semitic god, whose name was Tammuz.
(2) You're right about the etymology of these Hebrew-derived names. I think you're on shakier ground when you say that names ending in -elle are "not necessarily diminutive" in French; since the diminutive form exists, people are inevitably going to process those names as diminutives, regardless of the etymology.