A simple question, could a moon exist and stay whole if it was inside the ring of asteroids orbiting a planet? And as a side note, would it create a kind of bulge in the ring where the asteroids surround the moon? Honestly, this is entirely because my friend wants our planet to be uniquely pretty and I personally don't think this would work.
Ever heard of shepherd moons? Shepherd moons are moons (typically not very massive) that orbit in the middle of planetary rings, creating gaps in the material. They also keep the ring material where it is, rather than letting it dissipate:
Image courtesy of Wikipedia user The Viewer under the Creative Commons Attribution 3.0 Unported license.
Examples of shepherd moons include:
The list in the Solar System goes on.
See this video (which vanillagod beat me to) of Prometheus (right) and Pandora (left) orbiting Saturn by its F ring:
The rings extend beyond the edges of the image; these gaps are relatively small.
Yes, you absolutely can have a moon orbiting within a ring system. In fact, we have a perfect example of that in our own solar system: Saturn's A ring has the Encke and Keeler gaps, wherein orbits the moons Pan and Daphnis, respectively.
So if you want a ring system with moons orbiting within it, go ahead. If you want to make it realistic, just make sure to have the moons clear out sufficient elbow room for themselves, which will create a corridor wider than the moon(s)' diameter.
For comparison, the Encke gap is 325 km wide with Pan having a mean radius of 14.1 ± 1.3 km (thus mean diameter 28.2 ± 2.6 km) and the Keeler gap is 42 km wide with Daphnis having a diameter of approximately 8 km. It thus seems reasonable for such a moon to clear out a corridor with a width about 5-10 times the moon's diameter in the ring system. When viewed from some angle other than straight on, for any reasonably sized moon, this gap will be readily visible.
And because pictures get everyone's attention, even though it's small, here's a side view of Pan, courtesy NASA by way of Wikipedia:
and Daphnis from either above or below (hard to tell):
Particularly in the context of the picture of Pan, it's worth keeping in mind that the rings of Saturn are less than 1 km thick.
Depends on the moon. The rings exist because it is inside the Roche limit.
Any moonlet within the rings must be small and made of strong material so it resists being shreaded. How strong depends on how close to the primary you get. So, you might get a solid metal ingot able to withstand the tidal force, where it already came apart at any natural fissers or boundaries between different materials.
You can calculate the details for a specific situation.
Others have pointed out that such moonlets will have an effect on the rings.
I think the issue is how quickly the moon would GROW as it slowly accumulated mass from the ring. A moon is nothing more than a big chunk of debris in a ring, so it would attract the much smaller dust in the ring rather than slowly being ground down by said dust.
A stable "ring" of asteroids would imply the asteroids have little velocity difference relative to each other so chaotic collisions that could threaten the moon wouldn't occur, else the asteroid ring would just self destruct on its own, regardless if a moon was there or not.
If the "moon" is just the largest remaining fragment of a larger orbiting body that is still in the early stages of settling into a ring orbit post-fragmentation then it could be hit and break up further, but it would probably be an irregular shaped object, not something we typically characterize as a "moon" (although there are potato shaped moons out there).
Look at how folks think Mars "stole" it's moons from the asteroid belt. If you hypothesize that a planet, with an already existing ring system, could lure a larger asteroid into it's orbit like Mars did, then you could have both a ring and a moon, at least for a while. They would probably occupy different orbits but eventually the moon would attract and suck up all the ring fragments (or hit them and send them off into chaotic orbits, probably some would fall down and hit the planet, not good!)
It certainly is possible.
In the book "Planetary Rings: A Post-Equinox View" by Larry Esposito he talks about a "Ring-Moon"
ring-moon a moon near or within a ring
Found in the glossary of said book. This implies there must be a possibility for such a occurrence to exist and be physically possible.
Although I believe that this could not last too long as the moon inside the ring will slowly incorporate all of it's mass into his own while he orbits the planet faster than the individual smaller particles that make out the ring. On human scale this should still take a while so for a story there could be a moon inside a ring.
Consider this video of two Saturn moons about the bit with the bulge in the ring.