Is an online multiplayer mode for our game allowed, so long as there is no in-game chat and it follows all other rules?  Also, do we legally own what we submit if it is posted to Coolmathgames?

Hi squidchip! Multiplayer is allowed in games so long as there's no in-game chat.

When you submit a game to the jam, you own the game that you have made. If you are selected as a winner, there may be a conversation of making the game exclusive for Coolmath Games.