#1
It is a draw by the current rules. Of course that doesn't say why that rule is the way it is. Here is my attempt at an answer to this rule and some others.
When clocks were introduced into chess (OTB), overstepping the time limit resulting in a monetary fine, but the transgressor did not lose the game. People were not happy with that rule.
Later tournaments were held where overstepping the time limit lost the game. Period!
People were not happy with that rule, because, like in the position in your game, without a clock, Black could not possibly win. White would probably win without the clock, but it is possible for White to mess up. Hence, the compromise of a draw.
FIDE 6.9 says:
Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not
complete the prescribed number of moves in the allotted time, the game is lost by that
player. However, the game is drawn if the position is such that the opponent cannot
checkmate the player’s king by any possible series of legal moves.
In some other positions, the situation on the board overrules the clock - such as mate on the board, but flag has fallen. The mate wins.
FIDE 5.1.1 says:
5.1.1 The game is won by the player who has checkmated his opponent’s king. This immediately ends the game, ...
FIDE rules say 'dead positions' (no possible sequence of moves can win for either player) are draws, however computers cannot recognize all of these.
FIDE 5.2.2 says:
The game is drawn when a position has arisen in which neither player can checkmate
the opponent’s king with any series of legal moves. The game is said to end in a ‘dead
position’. This immediately ends the game, ...
This phrase "by any possible series of legal moves" appears multiple times in the FIDE rules, and one of the results of the rules is that a player can lose a game because of overstepping the time limit, and his opponent can demonstrate that there is a possible series of legal moves that checkmates (or the computer knows such). The rules in FIDE do not consider how improbable such a series of moves is!
People were not happy with this last situation. Indeed the USCF has for years had rules under the heading 'insufficient losing chances' that try to accommodate such cases. You can probably imagine the issues this rule caused at tournaments. The invention of digital clocks with time increment features helped solve the TDs problems. Just make the players play it out!
The latest USCF rules seem to be headed to removing the 'insufficient losing chances' rules.

