"has the floor" is usually used in formal situations, where in a group of people, it is one person's turn to speak and all the others in the group should be listening and not making comments. A moderator in a group discussion might say something like, "Peter has the floor now, when he is done it will be your turn to speak."
"Take the ball and run with it" means to take an opportunity and make it into something even better, or take an idea and expand upon it.