A podcast is just another form of content in a file therefore yes you can and the second part of your idea is going to need some form or subscription/payment process.
A quick Google and this article by Peter B. describes the general steps for setting up the podcasting environment, https://joomlabe.at/joomla-advice/management/how-to-podcast-with-joomla The ...
Pure Joomla doesn't allow this. You may try to find an extension
But there is a great chance there is no extension doing exactly what you want. So workarounds or customization will be needed.
On the other hand, Joomla allows to develop an extension to do what you need.