I currently have a WordPress installed at the root of my directory (like example.com) but I was wondering if I could install another one at something like example.com/new. Is this possible without causing any problems?
Yes, you can install Worpress into separate directory, but don't forget to change the default database prefix in WP setup process, otherwise it gets conflict with your existing Wordpress.
No problem at all. You can have 100 WP sites on the same account if your server can stand the load. Put each new WP site into its own subdirectory. Good luck.
you could have any number of installations on your same domain, make sure that they dont share the same database or prefixes to avoid conflict or issues. regards Josh