Tamarix dixit:
EXAMPLES
not everyone is permitted to go to X = non licet omnibus <DATIVE?> adire X
the sun shines for everyone = sol lucet omnibus <DATIVE?>
Everyone does it. = Sic faciunt omnes.
The discrepancy here isn't really with the forms of
omnes, but with the verbs and associated grammar of the sentence.
The verb for "is permitted" in Latin is
licet. It is somewhat unusual in that this is an impersonal verb;
paenitet - "it displeases" and
taedet - "it bores" are two other examples of impersonal verbs. With these type of verbs, the person affected is placed in the dative, so
licet omnibus = "it is permitted for all" -> "all are permitted."
The verb "shine" in latin is
luceo, and just as in English it is an intransitive verb (i.e. it doesn't take a direct object). To say something "shines on X" means that the shining is "to the advantage of" or "for the sake of" X; this relationship in expressed in Latin via the dative of interest (sometimes called the ethical dative or dative of advantage). So we use the dative
omnibus here. This is an important point, as there are a number of intransitive verbs in Latin which are used transitively in English (e.g.
pareo - "obey",
parco - "spare"). It is incorrect to use these verbs with a direct object in Latin (e.g.
pareo te is wrong wrong wrong!); most of the time, the word we would call the direct object should instead be placed in the dative (e.g.
pareo tibi is right right right!)
In your final example,
omnes is indeed nominative, the subject of the sentence.