Is there an iPhone app that will let me download music an ringtones without having to use a computer to sync them?
I download things to my phone all the time without syncing - (I have a dial-up computer connection). Under the circumstances, it's a lot faster than waiting for the computer!!
There isn't. The only way you cab do this is unlock/jailbreak your iPhone.
There is an app in iTunes which teaches you to make your own ringtones for free. I think it's called 'ringtone maker'.
All the apps that I know of require you to connect your iPhone to ITunes to sync your ringtones.