BS penalty. Int. grounding on Jameis.

It wasn’t clear that Landry was down by contact and then he rolled out of bounds. Winston should’ve checked whether the clock was running. Still, I didn’t know that a QB couldn’t spike it when the clock wasn’t running. Winston did mess up by spiking it in 3rd and short with almost 30 seconds left. That one made me more angry. Not only could we have allowed the clock to run if we had decided to kick a field goal, but also we might’ve been able to get a first down. I can only imagine that Winston thought it was 2nd down. He needs to be told to look at the scoreboard to check for running time and down and distance. He should know this, but apparently not.
Correct me if I'm wrong here. Once you snap the ball, the clock runs, correct? So, even if the clock was stopped beforehand, once the ball is snapped, the clock runs, you can spike the ball. What am I not seeing here? Other than another bad call by the refs?