My podcast was rejected....???

There is no obvious reason for rejection. The feed seems to be OK, though when I subscribed to it in iTunes the first attempt produced an error message saying it could not connect, though it was OK on subsequent attempts. If the Store met such a failure when it attempted to check the feed that could lead to rejection. The episodes are presumably all speech with no copyright music? Only the last one is flagged as 'explicit' so presumably the others do not have any strong or sexual language in them? - that again could cause rejection. I can only suggest that you check on the server to make sure it's reacting properly to requests, then try again in a day or so.

Incidentally, 'Performing Arts' is not a category but a sub-category of 'Arts' - you should change this: it's not fatal it being wrong, but it's likely to land up with your feed being in a random category.

It's possible that the Store is concerned that the music in question may be a commercial recording, and thus a breach of copyright. I would suggest adding a note to the overall description to say that the music is composed by yourselves . There are as you say many podcasts which seem to get away with using copyright recordings, but they do get removed if spotted, and of course the Store staff can't tell if music is in fact not a breach of copyright just by listening to it.

You've fallen over a bug in the automated part of the submissions process whereby you are told a feed has already been submitted even if it was subsequently rejected or removed. The workaround is to change the title slightly - you can change it back once accepted provided doing so does not change the feed URL. If you can change the feed filename, and hence its URL, this is also a good idea, as is changing the URL in the 'link' tag (this can easily be changed back afterwards). If you can't get this to work, go to https://itunespodcasts.zendesk.com/hc/en-us/requests/new and click the disclosure triangle at the right of the 'Choose a topic' field - choose 'Submission enquiry' as the nearest appropriate option and explain what the problem is.