To convert it to your religion, it's all a matter of waiting till your court bishop do its thing. Although it's more efficient if you assign vassals to take it over for you (counts for each county and a vassal duke answering to you), because that way each count will have his court bishop and the duke would have his own, thus all provinces would have separate chances to flip, instead of you having to wait till yoru single bishop convert all of them one by one
Cultural shift however is a far lenghtier proccess. What you have to do is, if I recall correctly, make sure that all counties are ruled by nobles of your culture, bordering other territories of your culture as well, and that said nobles preferentially have high stewardship to hasten the process. Over time the counties will start culture shifting by themselves at varying speeds. For example, during a game as the Byzantine Empire I was able to culture shift almost all of Anatolia and Egypt to greek culture by the end of the game.
Edit: Also, as far as I am aware building new holdings have no influence in province culture or religion, because it is merely an indication of whatever culture and religion the filthy, unwashed masses indetify with, not the landholding nobility.
