We just saw that the Beis Yosef brought rishonim discussing how was Yosef batel from perya verivya if he didn't have a girl; maybe it was midas chasidus. The bottom line is that the assumption is that Yosef kept all the mitzvos. Which leads to the question: did the shevatim keep the mitzvos? I've previously mentioned the Prashas Drachim by the author of the Mishna Lamelech, who demonstrated from many midrashim that Yosef and his brothers argued about whether they had kedushas yisrael or not: Yosef felt they did, and the brothers felt they did not.
Joel Rich, the audio shiur reviewer at Hirhurim, sent me a source that Yosef kept Shabbos: Eliyahu Rabbah Parsha 7 s.v. Baruch. I can add two sources: the Drisha from the above discussion - Yosef kept the entire Torah, and the Daas Zekanim Parshas Naso (Bamidbar 7:48 - Yosef kept Shabbos).
A famous question is who did the shvatim marry? See Pesachim 50a: "'And Yehuda saw there the daughter of a Canaani man.' What is Canaani? If you say literally a Canaanite, is it possible Avraham warned Yitzchak [against marrying a Canaanite], Yitzchak also warned Yaakov, and Yehuda will go marry a Canaanite? Rather, Rabi Shimon ben Lakish said it is a merchant." Ramban quotes this on Breishis 38:2. He also mentions a midrash that all the shvatim were born with twin sisters, and they married a shevet from another mother (because to marry the daughter of your mother is an isur of arayos for Bnei Noach, see Rambam, Melachim 9:5. Note that this would be an isur for a Yisrael.) This is also brought by Tur Ha'aruch on that pasuk. Ibn Ezra says they married women from Aram, Mitzrayim, Edom and Midyan, but not Canaan, except for Shimon, and that is seen from Breishis 46:10 - Shaul Ben HaCanaanis. (But from Rashi to 50:17, it seems more than one married a Canaanis.) A question on the ibn Ezra is that putting the issue of who is Jewish aside, the Torah forbade marrying people from Mitzrayim. Even though the reason did not yet apply - because they oppressed us when we were their slaves, the fact of the avos keeping the Torah was absolute and did not depend on the reasons for the mitzvos; we see Avraham had matzos and Yitzchak ate korban pesach, and the exodus from Mitzrayim had not happened! So why should they have married mitzriyos? For whatever reason, marrying a Canaanite must be worse than marrying a mitzris, whether it was due to the fact that Avraham said "from the Canaanim among whom we live, but they didn't live with mitzriyos, or for some other reason.