"1- Why isn't installation optional?"
Easy, if every console has a hard-disc and it gives you a significant boost you will use it because otherwise you would have to do a complete testing of the non-HD install which means you will have to go through every damn scene of the game and see to it that the resource loading doesn't result in framerate drops, long load times, etc. pp.
"2- Why is installation not allowed on the 360 (with the condition of having a HDD installed of course)?"
Equally easy if NOT every console has a HD you have to make your program run decently on a non-HD console anyway. If you did this, programming a version that uses HD will be extra effort without much return on investment.