There are a few problems here. For starters, the band didn't break up. Mercury left to record a solo album, which no one had a problem with because everyone was "burned out." And while the movie makes it seem like Queen reunited for Live Aid and hadn't even been speaking to each other, they had just released an album, "The Works" (which the movie totally omits). In fact, their last stop on their world tour promoting that record was a mere eight weeks before Live Aid.
As for Freddie's diagnosis, that likely happened between 1986 and 1987, meaning he wouldn't have known during Live Aid in 1985. Queen didn't put on a kickass show because they were reeling from the news of their lead singer's illness -- they put on a kickass show because they were fucking Queen.