basketball best scorer in one single game

The player you refer to is Mohammad Akkari, who played for Al Mouttahed Tripoli in Lebanon. He scored 113 points, on 32 of 59 shooting from behind the arc, in a game in a Lebanese league in 2012. This was the first FIBA Asia hundred-point game.

From wikipedia's list, the top several are children - U14 and U12 leagues mostly; most likely the highest by a professional player in a FIBA league (or equivalent; I'm not sure how far back FIBA goes) is Erman Kunter, who scored 153 points in a Turkish Super League game in 1988: see this very brief article about the game for more information.

Anat Draigor has the women's professional record at 136, though it's unclear what level the game was at (Israel's third level league, but I don't know enough about Israeli basketball to know if that translates to FIBA-level or not). She does officially have the Guinness World Record (to the extent that matters), so it's apparently good enough for them at least.