One word: impossible. Although I went to exorbitant lengths about a scientific explanation of Noah's flood in this question, but here it won't work.
Forget energy. The very concept is so immensely destructive, all life on Earth would be wiped out (except for some bacteria perhaps). Here is why:
Stopping The Sun Or Stopping Earth?
Your first question is about stopping the sun in midday. For this you have to actually stop Earth's rotation on its axis. As it happens, if you stop the solid part of Earth in one second, the momentum of wind and the oceans would literally rip things apart. The circumference of Earth is 24,901 miles. During 24 hours, Earth travels this much distance in a circular path. So everything on Earth (including oceans and the air) is rotating as a speed of 1037 miles per hour.
If you somehow stop Earth's solid mass from rotating (forget the energy and whatever), the momentum of air and oceans would be horrible. We are talking about a gale at speed ~1000 miles/h. For reference, category 5 hurricane has a speed of paltry 160 miles/h and the fastest wind speed recorded on Earth was in a cyclone at 255 miles/h. You can imagine yourself what would happen at ~1000 miles/h speeds.
And then the oceans. All oceans, seas, lakes and rivers would spill their waters eastwards at ~1000 miles/h. I don't want to go into the gory details, but it looks like most of (if not all) humanity would be killed in a very very horrible way.
Stopping The Moon
This one is no less disastrous. Even if you magically save Earth from the disastrous consequences of stopping its spin, this one would be equally deadly. Moon is the major source of tides on Earth. Stopping moon still around Earth on one spot would ... you know what ... start pulling it directly towards Earth in a straight line. Now talk about the one huge tide that would collect on one side of Earth.
Considering that moon does not slam into Earth and completely obliterate its existence within the 1 day of its stoppage, the huge tidal wave collecting on moon's side of Earth would destroy several cities. And once moon starts revolving around Earth again, that tidal wave would retreat and cause a horrible tsunami on the other side of the oceans. The ensuing destruction would be far greater than that of phase 1.
Furthermore, the tidal effect of moon's gravity on Earth's atmosphere can also not be neglected. Once concentrating most of the air on one side of Earth would create terrible storms and then suddenly releasing that amassed air to be equally distributed again would cause terrible storms again ... only in the opposite direction.
Foregoing the energy concerns for the task at hand, and the impossibility involving in delivering that energy to Earth and moon, the very consequences of carrying out the task would be so disastrous and immense that all multicellular life (exclusing some lucky flies or fleas maybe?) would be wiped out.
Deduction: Don't try this at home!