Can a pawn move to the last row diagonally without a capture? Playing the "Champion" J2ME chess, I noticed that the bot (black) made the move "Pg2-h1=Q." Is this a bug or just a rarely known rule like en passant and castling?
Pawns only go diagonally when they capture. See the section 3.7 of Chess rules.

The software you mention probably has a flaw.