I originally thought sleeping on the left side was recommended because of something for the baby, but after asking about it more I was told it is for us. There is a major artery or something that if too much pressure is put on it can cause the dizziness/faintness. Also, I am a stomach sleeper which concerned me, but my doc said as long as I was comfortable the baby was fine.
Not sure about your legs falling asleep fast, but makes sense because of the differences your body is going through with the pregnancy.