You can play solo, it's called Automon. This is just a multiplayer sequel. This game will also have an option to play against bots later, but not a priority for first alphas.
Capturing shouldn't be hard, but areas get exponentially harder the closer they are to the center.
Rest is like declaring a move to the area you're already in, so the other player also needs to move. If both players rest, it just skips the battle phase altogether and goes to the next turn of moving. If that didn't happen, let me know
If timer got stuck, it's quite possible that the server puked out an error - I need to implement some safeguards still, to let the game proceed even if that happens.