How durable are road or hybrid tyre tubes compared to mountain bike tyre tubes?
Having ridden both mountain and road bikes, I don't think tire/tubes designed for paved surfaces are actually any more puncture prone than tires designed for dirt or gravel, if used within their intended limits.

If you are getting frequent holes and tears in your tubes but not your tires, and you are not getting pinch flats, inspect the inside surfaces of your tires carefully for debris or small sharp objects that may be buried in the tire surface. if you run your fingers over the inside surface you can sometimes feel embedded objects that are not visible.

It's impossible to say how much faster you will be on different bike types on your commute. Also, speed is only one consideration, you may be more comfortable and happier on a hybrid with relatively wide tires and a riding position that allows better control than a slightly faster but more uncomfortable road bike.