iOS devices such as the iPhone, iPad, or iPod Touch do not work in disk mode as your old iPod classic would have in the past. If you have to transfer files between multiple computers and you don't necessarily want to use iTunes to add the documents/files to your iPhone, you may also look at this guide: Turn your iPhone into a USB flash drive There are a number of apps on the App Store both free and paid (USB Disk, USB Sharp, Documents, etc) which will make your iphone behave more or less like a USB drive though. Just install one such app and use iTunes to add any kind of file to your iPhone.
Could be a corrupt iPod music library file. If you have all of your iPod music already loaded within your iTunes library, try resetting the iPod via iTunes to factory settings. Next, sync the iPod with iTunes to transfer back all the tracks and playlists.
The issue might be either hardware- or software- related. If it is a hardware problem, your iPhone Wi-Fi switch under Settings > Wi-Fi will be turned off and/or greyed out (unable to be turned back on). This happens especially on iPhone 4 and iPhone 4S running iOS 6 and iOS 7 as the Wi-Fi radio chip overheats. Not much to do here except to take it to the Apple Store for replacement. If it is a software issue, it can get resolved by cold restarting the iPhone and/or by resetting your iPhone network settings via Settings > General > Reset > Reset Network Settings.