As for the price movement, I included bots in the game that move the price and provide liquidity by making orders. Even if there are only 2 real players playing against each other, the bots continue to trade and thus provide opportunities to profit from them. I don't find that the price stagnates until there is around 1 minute left, and even then sometimes there is some price movement and thus opportunity to profit.
The bots do have quite a bit of randomness in their decision making, so it could be that you got unlucky and they decided not to do much in your game. If this happens and you also don't decide to make your own moves on the market, it can end up looking like the market is stagnant.
Thanks for taking the time try my game and to provide feedback!