postcasts - can't find them on phone

I've been downloading some lectures (technically not podcasts) as mp3 files. From iTunes I right-click to "info", and change the "options" "media kind" to podcast.

First question: when I find the lecture within iTunes, if I delete it, nothing happens (no deletion occurs). What's going on here? I'd like to delete it so that I can start over (on my other problem, which I will get to). But the files are still there.

Second question, which is the important one here. I can't find the lecture on my phone.

Here's where I search for it:

That top hit ("The Rishonim: An Introduction (IV)") is what I want. So I click on it, and I get the general iTunes store, not my file:

If, within Podcasts, I search for it, it's not there.

What's going on? More importantly: how can I listen to the file that I downloaded, and which appears in iTunes, and in the search on my own phone?!?