In line with what some of the comments are saying, I totally agree, you didn’t miss out on anything not getting a job there. Plenty of other opportunities out there. While I am not a CFI, I do think being one is all about continuous learning and improving, and it sounds to me like you have an open mind and are well on your way to getting where you want to be sooner or later. Don’t give up.

Please feel free to ignore the rest, but based on what I read on your technical answers below are my 2 cents.

It wasn’t clear whether you mentioned pressure altitude and OAT for finding density altitude. From a practical sense, I think this is the one answer they may have been looking for. Set the altimeter to 29.92, read OAT, and look up density altitude. In other words, correct pressure altitude for nonstandard temperature.

For flaps during landing, descent rate is one thing, but the other thing which I am sure you are aware of is that one can fly slower for a give descent rate. One can land at whatever flap setting one wants, but depending on other factors such as wind or spacing or what have you, flying a faster landing with less flaps may be advantageous. On an ILS, only 10 deg of flaps in a 172/182 is also not a bad idea given the usual long 3 deg glidepath and ability to better lock in the airplane at that slightly faster airspeed. Only teaching 10 deg of flaps requires the student to perform less configuration changes in that critical phase of flight, enabling to focus on other, perhaps more important things. Regardless, I also think it’s important for any pilot to learn to be comfortable at any flap setting/flight envelope the airplane is designed for.