For RP, ESO class is best left out as the class style in ESO differes greatly from the 'classes' of the previous games and lore. Sme people recognize it, many dont. Biggest reason I always suggest avoiding it is simply because there is no sun magic, there is not holy magic, etc (see schools of magic). The spells you have you can use, but they are not templar skills they are restoration, destruction, and alteration (this also opens your RP to non-class spells)

Going with your concept, an Imperial who is a religious warrior would certainly be a part of the cult of the Divines, and thus oppose Molag Bal and most, if not all, daedra. Filling in the blanks on Imperial culture, look to Roman history. There is a very heavy emphasis on Imperials from the Romans.

Whether or not your religious view changes with Faction will very greatly. An Imperial is unlikely to worship the Tribunal, but may believe in the Reguard gods if they lived log enough with the culture. Someone like what I see your character as may even worship Meridia. IT is all dependent on where you live, how you were raised just like in real life. See your character as a living and breathing entity that can change, learn, etc. From what I can see, it is unlikely a Imperial 'templar' would be following a religion other than the Divines cult, but I do not know everything you want to do with yours character.

Speaking specifically on Imperials and culture, Cyrodillic Imperials are Cosmopolitan as many cultures find their way into the Imperial province. They are prideful of their country, but not in a manner similar to Altmer or dunmer whom are proud of their race and see themselves as superior. They are generally quite accepting so long as people of other cultures respect their laws as they would another people in their country. Imperial province is by far the most diverse and many non-Imperials will likely label themselves Imperial.

An Imperial from another province (most races exist throughout Tamriel), like any race in born or raised in another province, is likely to be adapted tot he culture of the area. An Imperial born in High Rock would act far more Breton than Imperial.