A podcast is basically a blog with RSS feed where all the entries are audio files. So in theory you could do it that way it’s probably be a bit of a job to set up, then serving the files would take a fair bit of bandwidth (if it gets even moderately popular), encoding to something like OPUS format might help if playback support in podcast players is widespread (MP3, AAC or OGG Vorbis might be a better fallback.
The audio editor I would choose is Audacity it’s been the gold standard for a free audio recorder/editor for years.
Careful with hosted podcasting services terms and conditions they can be restrictive with what you can do with your podcast later.
The amount of times I’ve seen this error over the last 5+ years, and until now I’ve not seen one comment mention it. Thank you you’ve restored my faith in people knowing what words mean. I’ve got to the point that if I see it in prose I stop reading because I assume the writer is an idiot.