I don't know where in the world you are, but here in the UK the medical advice is definitely to have them sleep on their backs until 6 months old. However, if there are no other SIDS risks (ie no smokers in the house - do a Google search on risk factors), you might want to let him tummy sleep. If not, the Miracle Blanket or Mothercare Swaddle Blanket are amazing. My LO was always on the 98th centile, really big strong boy, and it kept him totally wrapped until 5 months.
What happened between 4am and 6am? Why awake so long, what was going on?
Re the naps, how long is he awake in the morning before you start getting him ready for his first nap?