Unfortunately, I don't have a good answer for you, but I do want to encourage you and your son. My son was dx last May at 3.5 yrs old. He honeymooned until November when it was apparent he desperately needed more insulin. I wish we could go back to the days of little insulin, it made me feel like his body might be healing itself.
After diagnosis, we tested like crazy when he woke up, postprandial(2hrs later), before lunch, another postprandial, at dinner, before bed and then at 3am. We worked closely with the diabetes team at Children's Hospital in Seattle to adjust his insulin. He too would go low, and we figured out we could give him "freebies" with no insulin and this helped maintain him until his next meal.
In terms of how low you can go, I have heard of cases where for a period of time it seemed like insulin might not be a necessity, although over time the need arose again. Personally, at diagnosis my son was on 2 units of levemir (long acting) both am and pm and we figured out this was bringing him way to low and began reducing the amount, eventually we stopped the pm dose and reduced the am dose to .5 units. We also had a big reduction in his humalog, but have gradually increased his doses over time.
Every diabetes case is so individual, its hard to know what is causing his lows. At 13 his hormones may be playing into the situation (which we have no expereince in.)
Hopefully you have access to a CDE (certified diabetes educator), Dr. or Nurse that can work with you on making changes to his insulin. I would also recommend testing and documenting more frequently, to give you a better idea of his trends. This will also give the professionals the information they need to help make adjustments.
And finally, it does get easier, and way less stressful. It is so overwhelming at the beginning, and now I am learning to be more relaxed. I pray you have some relief from the anxiety that having a child with diabetes can cause.
-Best of luck