You are in a spaceship far outside our solar system. Inside your spaceship there is not gravity and no air (and therefore no air resistance). If you toss a ball across the spaceship, how do Newton's laws predict its motion will change as it moves?

According to Newton's first law, without any forces bodies save their state of rest or motion. Since you tossed a ball, it will continue going along direction of the force you initially exerted in a straight line. What would happen after collision with the spaceship's walls is frankly speaking unpredictable because you don't know configuration of the surfaces that the ball will hit, but what we can say is that after each collision the ball will move in straight lines.

Newtons first law: The ball will go at constant speed without stopping

Newtons third law: The ball will also push back at you causing you to go back as well