You'll change the title of the first podcast in the PowerPress settings for that show. You won't need to change any URLs or set up a redirect. The podcast title has no impact on your site URLs.
Yes, using a Custom Channel for the second show would be the best solution in your case. The second show's feed will be completely separate for the first, so changes made to the first show's settings won't have any impact on the second show's feed.
Yes, each show should have its own media hosting subscription in order to keep stats from commingling. If you decide to sign up for stats for the second show, you can use promo code SHAWN to get your first month's service free.
Note: if you've linked your WordPress site to your Blubrry account, you'll need to unlink it before setting up the second show, and if you were uploading media files directly from the WordPress site to your Blubrry hosting account, you'll need to instead upload files directly to your dashboard at blubrry.com and then copy/paste those media file URLs into your Podcast Episode entries on your website.