How do I deal with my parents in a way that fulfills my duty of righteousness towards them? What are the specifics of righteousness in terms of speaking and sitting with them, and should it be daily? Does my being considered an adult and responsible in the household count as overstepping their rights?

Filial piety is one of the best acts of obedience, and it is an absolute command whose regulation refers to custom. Thus, what is considered an act of piety by custom is commanded, and what is considered an act of disobedience is forbidden. You should strive to please them and speak to them in a way that makes you dutiful to them according to custom. If you spend on them the obligatory expenditure, there is no blame upon you. If they entrust you with a matter, do what you can of kindness, and seek what is most ideal and pleasing to Allah.