The remote site does not get the contents of your /etc/passwd if you do that, due to same origin policy. And you cannot see the /etc/passwd of the remote site. If you want to see your own, you can also open your /etc/passwd in vim. So, there is no vulnerability there.
The code I'm talking about typically calls `curl`, or similar, to download a remote URL, and show "stuff" about the contents.
I certainly don't expect to see my own file, but it is very common for remote sites to show THEIR /etc/passwd file, because they've used PHPs fopen function, or a curl-wrapper which didn't disable file:// URIs.
No. You can get the remote server's /etc/passwd in some cases. Most OS's would block a file that obvious from a non-privileged app but maybe /tmp/session.32eg3g3.txt is readable. There are sensitive local files that are readable by your web app so you must take precautions. This is in fact a common security hole caused by careless developers.