Analisa, about lying down - the first and main thing is lots of basic groundwork and building trust, the horse has to see his human as a true leader and feel completely safe around him. As soon as the horse is comfortable to allow the human to do just about anything and go anywhere with him, we can start thinking about lying down, because it cannot be done until the horse feels completely ready. Also, he has to be taught lowering the head beforehand. Then, as it was done with Snickers and several other horses - this can be done after a ride or an active groundwork session, or in a rolling spot, when the horse feels like rolling. Lower his head gently and tap the ground rythmically, focusing on the ground and keeping the concept of how nice it is to roll in your mind. Let the horse think, he should soon try to understand the tapping and paw the ground a bit. That's enough for the first time - at that moment lots of praise is appropriate. Maybe the horse will lay down at the very first time, but, if not, the next times you can start encouraging him to think about lying by giving a light tap on the front leg that is not pawing at the moment. If the horse feels ready, he understands the concept pretty soon. At first the result will be just lying down and rolling, but, when the horse is comfortable with that, you can start keeping the lead rope over his neck during the rolling and inviting him with light pressure to stay on the ground, when he feels like standing up. Even later, you can progress to lying on tummy, not on the side, sitting, letting you mount while he is lying, etc., but complete trust and patience are crucial in this. :) And no ropes around legs needed.
I have come a long way, to surrender my shadow to the shadow of my horse.