I noticed in Shemot that HaShem first introduces himself to Moshe as the G-D of his father and then separately as the G-D of each of the Patriarchs. Also, in Shemot, the Torah speaks of a "man" going to the tribe of Levi and taking a wife (its assumed it was Amram, Moshe’s father) and lastly in Vayeira, HaShem says that the Patriarchs didn’t know him as HaShem, only as Sha-dai (related to natural miracles). Does HaShem have to tell Moshe who his is because the patriarchs (and descendents) would not have recognized HaShem as one who performs unnatural miracles such as the burned (but unburned) bush, the staff into a snake and the ten plagues because Sha-dai never exhibited this attribute and because Amram isn’t initially mentioned as Moshe’s father until later and this corroborates that Moshe is Hebrew?
The questions you ask deserve a broader forum than this answer but I will mention some points. The idea of mentioning the patriarchs as a group and then each one is not uncommon, and in fact is the form used at the beginning of the Amidah prayer. This may indicate that man relates to G-d as part of a group ( in this case the family of Avraham) but also each man finds G-d as an individual who has a unique relationship with the Creator. Mentioning this at this juncture points out to Moshe that although he is embarking on a national "project", onbe must keep in mind individual suffering and worth. 2. Your interpretation of the patriarchs' knowledge of Sha-dai as not knowing G-d's miraculous manifestations is consistent with several commentator's views. Whether Moshe was aware of his Hebrew roots is a matter for speculation.