I'd like to customize the feed URL of a certain Wordpress-based blog that I don't own in order to show all posts ever published. This is because I like that blog and I want to read everything the author has written, without missing a single post. Is this possible? Or should I surf this blog manually? Thank you.
No not possible. WordPress gives the owner of the site control over how many posts to show in the feed. The default is 10
If you want to be able to read rss feeds from other sites then you should not worry about changing there settings. Instead use a service like Google Reader. If you want to share that post then create a post with a reference to the original content and make sure you have there permission to do so.
I will offer two solutions, the harder programming one, and an easier service-based one.
If you are good at programming or the command-line (using cURL, perhaps), you can take advantage of the fact that most recent WordPress blogs will respond to something like the following:
where X is the page of posts that you want. As the other posters stated, you normally only get, say, 10 posts. But with the paged query parameter, you can iterate through 1, 2, 3, ... until you get to a page that says that it was a 404 (page not found) request. These requests will give you the XML that the feed normally has. You can try to parse the URLs out. Once you get all of the URLs for the blog, you can try to run them through something like Yahoo! Pipes to create an RSS feed that you can subscribe to. I think this will mostly do what you want.
If the site owner uses FeedBurner, things are a little more complicated. Basically the blog is set up to redirect to FeedBurner unless it believes FeedBurner is trying to access the blog, in which case it will return the normal feed. If you are trying via the command-line or programming, you can try to spoof the blog by pretending you are FeedBurner by changing your user-agent. Needless to say, this all is probably not the easiest solution. ;)
Service that you can use
Alternately, I have been working on a service that should do all of this for you. It's still early in development, but it might help. Feed Rerun will let you put in the URL of a blog and you get a feed that you can subscribe to that will make a post every other day from the beginning of the blog up until today (in order.) Each post will link to the original blog so you can read it there with the comments that were made. It will get better over time to add more features and blog types.
Let me know if this answer helps!