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  3. Loss on time running out when it should be a draw according to FIDE rules

The FIDE rules says that in order to lose on time there has to be a series of legal moves that can lead to a mate for either player. In this position lichess.org/3aGexfKU/white#96 my time ran out but there it is not possible for either player to check mate the other through any series of legal moves. According to the FIDE rules this should be a draw. Wondering why that is not the case here on Lichess.

Edit:
In case anyone is not familiar with the rules you can read them here: www.fide.com/fide/handbook.html?id=208&view=article

And article 5.2.2 states the following "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, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7."

Article 6.9 states " 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 thatplayer. 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."

True though I think it will be quite tough to implement it. I had a position of similar nature (blocked pawns with a bishop that cannot sacrifice for a pawn) in Atomic chess and the game was ruled as loss for me :(

It has to do with the difficulty of arbitration. The site sees only that Black has sufficient material for mate, it won't evaluate the position.
Another typical example is a position where both players have pawns that block each other and opponent's King from approaching. Pawns can't be exchanged nor attacked, neither advanced. Only Kings can move around on their own side of the board. Yet because both players have pawns (sufficient material), it won't declare a draw when either player runs out of time.

Sure. Indeed this would be a draw in RL.

For example moving and overstepping the time.

Indeed, I'm still working to fix this (this can only be resolved by an unbounded search):
github.com/ddugovic/Stockfish/tree/helpmate