How to delete a single episode of my podcast?

You can simply delete the episode from your feed and add a new one, then re-uploaad the feed. New subscribers will see the change immediately; the iTunes Store will take a couple of days or so to catch up. Of course if you have any existing subscribers who have downloaded the episode they will still have it.

Don't delete the episode and then have a delay before adding the new one - if that were to go on for some time the podcast might be removed from the Store.

When you come to add future episodes, just add them and re-upload the feed. At no point do you have to re-submit the feed (indeed you can't).

I'm not familiar with Podomatic, but you should have no difficulty deleting the episode, and then adding a new one using the same process you originally used. They would then re-publish (same thing as upload) the feed - either automatically or perhaps you have to click a 'Publish' or similar button. If it's not clear you would need to look in their Help.

You can't edit anything in iTunes: it simply reads the feed. You have to make any changes in Podomatic - simply change the details in the same place you originally entered them.

Changes will take a couple of days or so to appear in the Store so don't panic when it's not immediate.