Can I edit title or icon of rss podcast (as a listener)

Got 'em. I think they're hiding in New Zealand. (Hopefully, that sounds funnier {and less creepy} than "I know where you are"! If not, put it down to British humour.)

You are correct, they are two separate feeds, for two distinct shows. However, as you say, each one has the same "programme name" and to the uninitiated, it looks like the same URL, even though they are not.

It looks as though the producers have been a bit lazy, or perhaps they simply don't understand what they're doing. They certainly haven't looked at their Podcast output from a listener's point of view and therefore failed to notice the limitations of their endeavours. Sadly, they are not the only ones guilty of all three of the aforementioned, I can assure you.

As you note, on the Podcast RSS list page of their website, every Podcast show looks as though it has the same URL, but the actual link is different. That's poor as well. Someone having trouble find their Podcast in a Podcast app might get as far as that RSS page and simply type what they see into their Podcatcher app. For example, I use a non-Apple podcatcher app on my iPod and when a search of the app's browsing section fails to find a particular podcast I'm after, I often end up at the producer's website on my desktop and then simply re-type the Feed URL into my Podcatcher. Of course, I need to type in the precise URL, but Radio Waatea is not showing the precise URL. Oh dear!

It does appear that the station needs to tweak something. Unfortunately, experience tells me that suggesting to them that they might need to make some adjustments in order to improve is unlikely to have any impact. I don't suppose the take up of their large output of Podcasts is too high. Consequently, they won't invest money in improvement. I wouldn't be surprised to discover that they're only providing Podcasts because "that's what everyone else is doing". Once again, sadly, they're not the only ones.

What a sad state of affairs. Nevertheless, you could try contacting them and see if I'm wrong.

To return to your original question: can you edit the title?; I've just tried it and the answer is no. In the screenshot below, I've previously edited the title, but as you can see when I look at it again, although my edit is still present, it has not changed the title in the main window:

That's not all. When I downloaded an episode (and no, I cannot speak Moari), I thought it was taking a long time to do so. If you look in the screenshot below, the episode highlighted in blue is six minutes long. However, until I downloaded it, it stated that it was only 50 seconds in length, as do all the other episodes. And no artwork either.

Thanks for posting this. I've enjoyed examining this so that I could provide an answer for you. It's a pity that I can't be the bearer of better news.

I don't believe there is.

Is it possible that the podcast has changed its host services and one feed is the current one while the other is an old one? Check the dates of episodes in each feed. If there is no overlap, but episode numbering (if provided) looks contiguous, that suggests one feed has in fact replaced the other and there isn't much you can do about it except remember the situation. Alternatively, I suggest you contact the show's producer to see if you can get more information.

As for the icon, if I search for Radio Waatea in my iTunes (here in the UK), iTunes goes completely blank! It doesn't even say "no results found". If I look on Radio Waatea's website, I don't find anything resembling your description. All very mysterious. However, if I search the store for "Podcast411", among other results, I find this:

which appears to have nothing to do with the one you have. Perhaps they have just used a generic icon (which isn't a good idea).

You're welcome.