Yes, you can install a "one-click" phpbb to a domain where you have already installed WordPress. There are two things you have to realize for this to work, however. First, you cannot use "one-click" to install to a directory that already contains files, so you cannot use it to install phpbb into the same directory into which you installed WordPress.
You can install it into a different directory (ususally a subdirectory, but it could be your "main" directory if you installed Wordpress in a subdirectory), though if either the Wordpress or the phpbb is installed in your "main" directory, you could create issues that might be hard for a beginner to get sorted (.htaccess re-write rules, etc.). For this reason, I suggest you either install both of the applications in subdirectories, or install one of them into a subdomain, which is your next question
No, as I described above, you can use subdirectories instead. It is important you make the distinction between subdomains and subdirectories. If you have your WordPress already installed in your "main" (or "top") web accessible directory, I think you will save yourself some potential headaches by using a subdomain, maybe something like "forums.yourdomian.tld" or similar. That way you will never have interaction between the operation of the applications' .htaccess files (which often re-write urls and can complicate things considerably if you don't fully understand how they work). Good Luck!