Thank you, Vitaliy (and sorry for not replying earlier - I was on vacation :)! I turned disable_path_info OFF and then I was able to create a custom page!
P.S. In the process, after turning off the disable_path_info, I got “Failed AJAX request or invalid JSON returned” error when trying to click anything on the “Navigation Menus” page (like described here: Failed AJAX request or invalid JSON returned), but I turned disable_path_info on and off again, restarting Apache service after each change, and then the AJAX/JSON error disappeared.