1) How does the Gemara know Reb Meir was Acher's
talmid? The questions posed on 15a were posed by
Acher to Reb Meir?
It looks like Acher was asking rhetorical questions from Reb Meir and Reb Meir was trying to avoid the subject, and only addressed Acher's status as a rasha when Acher showed from Reb Akiva that the Psukim were talking about reshaim. Do you agree? Again, no real mention of Rebbi Meir being Acher's talmid.
Although Reb Meir followed Acher on the horse on Shabbos, maybe he was just trying to get Acher to do Teshuva. Again no proof that he was his talmid.
2) If indeed Reb Meir was Acher's talmid is it
possible that "Maan Acherim Reb Meir" that is stated
numerous places in Shaas is a hint that these
statements came from Acher & Reb Meir?
Yasher Koach
Chaim Ozer Shulman
1) You are asking how the Gemara knew that Rebbi Meir learned Torah from Acher, until it asked how he was permitted to do so. Perhaps he just rebuked him and the like. It could be that the Amora'im here had a tradition that Rebbi Meir had been a Talmid of Acher; Rebbi Meir was near the last generation of Tana'im and certainly the Amora'im were familiar with those Tana'im's histories.
2) TOSFOS in Sotah 12a writes what you suggest, that when the Gemara (end of Horiyos) says that "Acherim" is Rebbi Meir, that means Rebbi Meir stating Halachos that he had heard from Acher. (Tosfos later rejects this approach.)
Mordecai