Yes, 16 days should be plenty of time in my opinion.
I have driven the ring road several times, sometimes in much shorter time, but then of course not with quite so many activities.
I took a brief look at your itinerary and it looks quite good. It covers many interesting places, although I would strongly recommend you to consider visiting the magical and beautiful Snæfellsnes peninsula. It's a little bit off the ring road, but it is worth it.
Although I don't have personal experience with camper-vans, I don't think you'll have any problems there. Travelers are usually allowed to park their camper-vans for the night in most places except close to residential buildings, protected areas, and on cultivated land. The best spots are often found taking side roads a little bit off the main ring road. There are also plenty of official campsites when you need facilities or you can't find any suitable spot. It's a great and flexible way of exploring Iceland. There might be days when the weather is bad and you would want to change your plans.
Drive carefully, especially when entering one-way bridges and on dirt roads. And make sure to have enough warm clothes, it. It can get quite cold in September, especially in the north.
Hope you have a great trip!