Is there any way for Black to win from this position?

https://www.chess.com/analysis/game/live/5804127728?tab=analysis

At your level, there is always a chance/way to win.  So yes, in that position back has chances to win. 

The final position should be winning easily for white, he has an extra rook and an extra pawn. If 42.Qxe5 instead of 42.Bh3 it's close to being game over immediately because the queens will be traded and black will no longer be able to generate any kind of attacking chances. Then the extra material white has should prove easily winning. I'm not sure why a draw was agreed to in the end here. 

Any chance?

Flagging or gross blunders by white.

Realistic chances?

Not really.

Drawing chances?

Possible at this rating level even if flagging is not an issue for White.  It depends on whether or not White can come up with a winning plan.

Best guess for how this happened?  White was close to flagging and offered a draw that Black could not risk refusing.

no not possibile

Black is completely lost. 42 Qxe5 would have been easiest for white. In the final position, black has no moves. ...Bg6 may delay the loss for a move or two and white can still force off the queens and promote a pawn.

If you look at the ratings of both players (700) of course black has chances to win.

yeak