Do I have to download each individual file manually?
No. There a multiple ways you can access the files but by far the best way is to Subscribe to it using the service of your choice, i.e. itunes, etc.
For people who are not interested in subscribing, every episode may be streamed or downloaded directly from the Grammar or Medical Spanish links. These links are found under the Podcasts link above. From the Grammar or Medical Spanish podcast page, you man click on an episode title. This will open a new window with the audio player and tanscript (show notes) for that episode. Now you may read along as you listen.