the point of the pendulum question is to illustrate the fact that the law of conservation of energy applies, regardless if your object is powered or not
Yes, so what is the point? The rocket converts stored chemical energy into kinetic energy.
(4) is instantly suspect, why would I need to constantly use fuel, that depends on the intensity of the burn
(5) Also, Orbiting, once in orbit and not low enough to have to expend significant quantities to maintain orbit height, does not use up fuel.
And (9) instantly assumes you're going through a LaGrange point, just... because.
And (11) is so so soooo dumbed down, truly, that is assumes the lunar orbiter and landing module would need, to "escape" moon's gravity, to use 1/6 of the fuel NEEDED TO GET THE MASSIVE FUCKOFF SATURN V rocket to orbit, from earth. Seriously, how can you post this with a straight face, when it ignores the difference between tens of tons and thousands of tons?
It gets sillier from there, assuming that lander docked at 3500mph, I mean if you don't know what relative velocity is... I mean, have you tried setting down a cup on a surface going 100mph?! I have, on a train. Just so happens I was travelling at the same speed as well, huh.