Singing with your eyes closed is not bad and is, in fact, somewhat traditional.

Depends on where you are singing too. If you are performing in the mainstream music world, especially in the United States, the audience expects you to entertain them, put on a happy face and smile. If you are singing at a session in Ireland you're apt to close your eyes and maybe grasp the hand of the person standing next to you (more acceptable if you know the person, of course).