Can't change permission on Time Capsule files and folders

Question

I am using my Time Capsule as a storage device that everyone on my network can access, and I also have a fairly small (~5000 songs) iTunes Library as well. This was all working fine, until I decided to try to get a second computer, beside my MacBook Pro (8,1) to connect to the iTunes Library. Suddenly strange things started happening, like the network dropping at seemingly completely random times, certain people being kicked of the network, etc. So then I thought "well maybe its because of the iTunes Library." So I did a 'Get Info' to the Library folder, named iTunes Library, and it showed this:
This didn't seem too strange, except for the (unknown) name. I then learned (http://pondini.org/TM/E10.html) that this may actually be causing the problem, so I hit the minus button while hovering over it, only to see this:
Now, as far as I can tell, this shouldn't be happening. So I tried it on many different computers (10.8.4, 10.6.8, 10.7.5, among others), and they all said this. Then, back on 10.8.4, I decided to try to add my name, even though it said that everyone can read and write, and it said this:
Now I knew this was strange, since it has never, ever happened to me since OS 7. What was also strange, instead of showing the usual selection window, it asked me to type in my username, like so:
This happened on every computer, and in every directory and every file (or at least the couple dozen I tried, including ones outside the Library folder that I had already changed permissions on before normally), so I knew something was definetly up. So of course, I turned to my friend, the Terminal. I tried doing sudo chmod 555, 755, 775, 777, and a+x, and none of them worked, again, on multiple different files and folders. Also, since I have connected the second conmputer to the Library, it seems as though the file iTunes Library.itl is no longer executable, because it looks like this:
Also, no one but me can connect to it anymore, even though they can all see it. Any help would be greatly appreciated.
EDIT: Sorry for the low-res images, Apple seems to have done something to them

Answer 1

Verify volume failed with error Could not unmount disk (-10000)
That could happen if there is another process that is presently accessing the volume.  I don't think it related to the volume having data corruption.  The fact that is it a "server" may be relevant.
In the time that you have had this problem, has it been shut down and restarted? 
You can also try restarting it with the Shift key held down.  That should do a Safe Mode startup, if an Xserve acts like a regular Mac.
http://support.apple.com/kb/HT1564
http://support.apple.com/kb/HT1455
The Safe Boot will do some maintenance and tests during startup, and start up with only essential proceses running.  Try accessing that folder now.  If you can access it, you should probably save it off on another volume, such as an external drive, so that you have a current backup.
Try running Repair Disk Permissions and Verify Disk again in Disk Utility.  Repair Disk Permissions will probably give you a lot of messages; they are usually just "informational" so don't be concerned.  However, if Verify Disk reports an error, that is a serious problem that needs to be addressed.
Edit:  If the volume being tested is NOT the startup disk, then Repair Disk Permissions will be disabled.  It only applies when there is a system installed on that volume.