For language : As occitan-speaker i can understand a great part of a catalan speech.
Of course they're some differences and it's distinct languages, but the difference is due to prononciation, some graphic different uses, castillan/french influence.
In the timeline i'm working on, i would make catalan, due to different cultural expension, rather a franco-provencal regards french situation for occitan : not really just another dialect, but not a complete distinct language.
And, no, Provencal is really closer to all other occitans dialects with a virtual 90% (in radical cases) of inter-comprehension. Only graphic differencies CAN cause some difficulties. But in oral, no problems. Provencal is a dialect, not a language.
For prononciation, some uses are settled in vertical zones, as one sound use in Gasconha and Western Catalunya, others in Lengadoc and Easter Catalunya.
For further explanation, Pierre Bec have made vulagrizing books on occitan. But i don't know if it were translated
For a state : somes possibilities
Early Middle-Ages : surviving Kingdom of Tolosa
High Middle-Ages : surviving Kingdom of Aquitaine
Classic Middle-Ages : victorious Kingdom of Aragon in 1213 ( Battle of Muret) or a Burgondy-like destiny for Raimondine dynasty?
French Revolution : Girondine sucessful creation of "République du Midi" (a real proposition made by few revolutionnaries, not an occitan republic, more meridional french oriented)
Maybe you can work with a surviving occitan Poitou. Due to diseases ofr High Middle-Ages, to the continual invasion of Aquitaine by Franks who make Loire zone depopulated (much like southern Asturias in early reconquista), occitanophone population was replaced by francophone colonization, until Gironde.