Yes, and so did Apollo 12, 14, 15, 16, and 17. The Apollo spacecraft were built to go to the Moon. The space shuttles were not. They were built as reusable craft to go back and forth to the space station and perform other missions in Earth orbit.
The SIX manned moon landings weren't faked. 400,000 people were involved in making the Apollo 11 moon landing happen. The Apollo Moon landings were among the most completely documented and observed events in history. The conspiracy "theories" that claim otherwise are a bunch of nonsense without even a single compelling piece of evidence. Most of the questions raised are based on ignorance of basic physics and optics.
Video special effects were in their infancy in the late 60's so that faking a landing on the Moon would probably have been more difficult than actually going there, and it seems highly unlikely that the hundreds or even thousands of people who would have had to be involved in such a conspiracy would have kept it a secret for so long. Ultimately you'll have to decide for yourself if the marginal evidence offered to show this was all a hoax is compelling enough to overturn the overwhelming evidence that it actually occurred, but make sure you check the facts carefully, you need to be a little skeptical of the skeptics, too. For more detailed debunking of this ill-conceived notion, see sources.
The answer is, it isn't waving. It looks like that because of the way the flag was deployed. The flag hangs from a horizontal rod which telescopes out from the vertical one. In Apollo 11, they couldn't get the rod to extend completely, so the flag didn't get stretched fully. It has a ripple in it, like a curtain that is not fully closed. In later flights, the astronauts didn't fully deploy it on purpose because they liked the way it looked. In other words, the flag looks like it is waving because the astronauts wanted it to look that way. Ironically, they did their job too well. It appears to have fooled a lot of people into thinking it waved.
The reasons that we haven't been back are cuts in funding, we had done what we set out to do, and we had refocused on the space station and the shuttles. We are going back in 2020 and establishing a lunar base as part of Project Constellation. We will be using new modular craft, the Orion, with the Ares launch vehicles, and the Altair lunar lander. There is a projected manned mission to Mars as well.