Installing WordPress only for a separate page – ‘mydomain.com/blog’

Completely possible. Say you have domain.com. You set up a WordPress installation in domain.com/my-special-page, and you will be able to access your WordPress site there.

You can ALSO set it up at domain.com/my-special-page.php if you really want to keep file name extensions, but it’s more work, and an uglier URL, so I wouldn’t recommend.