The Maimonides Reader (p. 478) quotes Maimonides' responsum to Hasdai Ha-Levi where he states that our forefathers didn't keep the mitzvos at all.
Where else can this responsum be found? (particularly in the Kovetz t'shovos haRambam v'igrosav, the Blau responsa, or the P'er Hador responsa).
The Rambam explicitly lists the pre-Sinai commandments kept by the abhoth in Hil. Melakhim 8:1:
Six precepts were commanded to Adam; the prohibition against worship of false gods, the prohibition against cursing God, the prohibition against murder, the prohibition against incest and adultery, the prohibition against theft, the command to establish laws and courts of justice.
Even though we have received all of these commands from Moses and, furthermore, they are concepts which intellect itself tends to accept, it appears from the Torah's words that Adam was commanded concerning them.
The prohibition against eating flesh from a living animal was added for Noah, as Genesis 9:4 states: 'Nevertheless, you may not eat flesh with its life, which is its blood.' Thus there are seven mitzvot.
These matters remained the same throughout the world until Abraham. When Abraham arose, in addition to these, he was commanded regarding circumcision. He also ordained the morning prayers.
Isaac separated tithes and ordained an additional prayer service before sunset. Jacob added the prohibition against eating the sciatic nerve. He also ordained the evening prayers. In Egypt, Amram was commanded regarding other mitzvot. Ultimately, Moses came and the Torah was completed by him.
I personally have not read the responsum, but if it exists and says thusly, it wouldn't contradict his ruling in the MT.
It is present in the Sheilat ed. of Rambam's responsa (p. 673 IIRC), but R. Sheilat demonstrates that this responsum is probably a forgery.
See, however, Tzvi Langerman's piece in which he argues for the authenticity of the responsum.
Bnei Noach cannot "keep" a mitzvah as a mitzvah.
All of humanity including bnei Yisrael were commanded in the sheva mitzvot bnei Noach(the seven laws of Noah). That doesn't mean they didn't do things that were similar or maybe even exactly like mitzvot today. Things started to change with Avraham(Nedarim 31) and no longer considered bnei Noach.
For instance, Avraham instituted and did the Shachris morning prayer, but was not commanded to him to do or to pray.
I can't remember the exact citation, but it's similar to Hilchot Melachim 10:10, where it says a (shomer sheva mitzvot)ben Noach can do any mitzvah he wants even though he's not commanded, so I can only assume this is the case with the most ger tzedek of them all: Avraham.
Also, from a really mind-trippy view, because the Torah was not given yet, Sanhedrin 56b states that at the waters of Marah is where bnei Yisrael received the sheva mitzvot. What blows my mind is that we learn about this through the Torah, so anything we learn from the Torah before Torah gets tricky. It's kind of like saying, "Did anything exist before Torah".
