Would it be possible to have an object orbit inside Earth's atmosphere

Well, it doesn't have to be Earth's; just any atmosphere.

Would it be physically possible for a body (such as a meteor, moon, etc.) to actually orbit so close to a planet that it's inside it's atmosphere?

No. The friction from the atmosphere would quickly slow it down and it would crash. The principal reason satellites leave orbit is from friction from even the very tenuous atmosphere at their altitude.

It is possible for the LHC to create black holes that orbit inside the Earth, not just inside the atmosphere. At the speed required to orbit, any normal sized object would be (ignoring sub-atomic particles) rapidly either burned up or slowed down. So for normal matter, the answer is "yes, but not for long". There are some theories that suggest that magnetic monopoles or dark matter could be orbiting inside the Earth. None of these scenarios are likely, however, but absence of evidence is not evidence of absence. "Not for long" meaning 10's or 100's of miles, not multiple orbits.

Sure.

"Orbiting" means "going around".

Ships do it, airplanes do it, hot air balloons do it, even people do it (walking).

Phileas Fogg did it in 80 days.

When you ask questions, make sure you thought them through first........

Yes, but it needs the correct velocity (speed and direction). the closer to the earth it is, the faster it needs to go in need to orbit

You mean, like the ISS or the Hubble Telescope or any number of satellites in orbit within Earth's atmosphere - since they do it must be possible.

Why does everyone think the LHC creates black holes?! Nothing on EARTH is powerful enough to force matter into becoming that dense.

Yes, yes it is.