1) The Gemara talks about a Ger who was converted amongst the non-Jews and
didn't know about Shabbos is chayav a korban chotos. How could that be? If
we convert a non-jew we have to teach him some of the smaller and larger
(Mikzat kalot v'chamurot) of the mitzvot. Certainly the concept & laws of
Shabbos should be included in the chamuros. I saw Tosfos on this but was not
really satified with the answer.
2) Munbaz - Is this the same Munbaz who was a famous ger & was King of
Adiabene, (his mother was Queen Helena of Adiabene)? He contributed kaylim to
the Beis Hamikdash. Was he a Tanna also? If so, the time period doesn't
quite fit with Rabbi Akiva who lived a generation or two after the churban.
1) Tosfos (68a, DH Ger) says that learning the Mitzvos does not prevent a Ger from being a full-fledged Ger. In order to become a Ger, two requisites are necessary: acceptance of the Mitzvos, and learning the Mitzvos. Acceptance of the Mitzvos is certainly necessary; without it, his conversion is invalid. He must accept the authority of Hash-m and to fulfill the Mitzvos. He does not have to know what the Mitzvos are, in order to be considered a Ger (just like the Jewish people at the time the Torah was given, when they said "Na'aseh v'Nishma"). If Beis Din did not inform him at the time of his conversion of some of the less severe and some of the more severe commandments, he is still a valid Ger. (See Magid Mishnah, Hilchos Isurei Bi'ah 14:1)
See also the RITVA, who also says that Beis Din did not have a chance to inform this Ger about Shabbos. He adds that it could also be talking about a Ger who had been converted by Beis Din when he was a Katan.
2) You are correct. Munbaz the King was not a Tana.