lol... I thought it woud be obvious that this is not a "lying on your back with arms extended waiting for the opponent to do whatever they please" posture. It's from the boxing set, turned on its side, and not showing the opponent.
From mount defense, the left arm is trapping the opponents right arm against your body so they can't brace when flipped, while the left leg hooks on the same side, and the right arm is hooking around the opponent's back for leveraging the turn. That's a standard trap and roll escape in BJJ, probably the most common and first you learn. There are other variations from the closed guard position with the hands doing other things, depending on the position of the opponent, that can easily turn into triangles, arm bars, or escapes to standing.
As far as using forms for fighting applications, that's what they are, a library of techniques. In BJJ there are hundreds of techniques and you practice the same movements solo as you would apply. It's practicing form.