1 - The one click installer will give you a chance to install in a subfolder. Example.com/wordpress or example.com/blog etc.
2 - yes install wordpress in a subfolder.
3 - Use use the dreamhost panel Googies > htaccess/WEBDAV to set a basic password for the SUBFOLDER that you installed wordpress in. Don’t confuse an htaccess password with real security tho, but it will keep nosy people and automated bots out of your wordpress site that you are testing. (Important: Do NOT check the “Enable WebDAV on this dir?” box when setting up the htaccess password. WebDAV is something else entirely and enabling that box will create a problem where the best answer is “start over”.)
4 - Wordpress Codex has instructions for moving index.php https://codex.wordpress.org/Moving_WordPress There are really two steps in your case tho. First remove the htaccess password we set above, then follow the instrauctions to move index.php up to the root level of your site.