#1 What you are talking about is not a bug but a difference in rules between lichess and FIDE regarding rules for drawing.
FIDE rule: Game is draw when your time run out and there is no legal sequences for opponent to mate your king.
In online play without arbiter, FIDE Online Arene is using this rule solely to all extent.
http://support.premiumchess.net/how-to/draw-casesThe disadvantage is that many positions where you have to play very very stupid and actively help your opponent to mate you will be judged as lost, making this rule be a bit silly if applied to that extent.
The lichess rule has the disadvantage that it judges certain positions where there is a forced mate as a draw.
A compromise could be letting a comp do a fast eval and judge draw if there is no forced mate and win if there is a forced mate.