I don;t get why you get the average of enthalypy on the 1st question. Is it because the h2 is the "end enthalpy" of the system inside so h_exit should be between h1 and h2?
I explain this at 2:20. So in simple terms, we need to make assumptions, one such assumption is that things "won't change." So to get that, we need to average out values, otherwise, solving these problems would require a lot more work, with time rate differences.
It's on my to-do list, but I probably won't get to it for some time. There are a lot of videos on mechanics of materials on RU-vid. Have you looked through them as well?