Hi, regarding CF7 plugin not sending emails, please try disabling “Anti spam” option in HMWP General settings tab. Also set “Email sender name” and “Email sender address” fields to your valid name and email.
Applying “medium privacy” settings scheme from HMWP start tab should be fine. It will not change the paths for post, category, tag, author and feed. You can set with paths to rename and which not in HMWP “Permalinks & URLs” tab.
You can use another security plugin like Wordfence, ithemes security, all in one wp security, etc. along with HMWP. We recommend you to use Wordfence.
But make sure that you do not enable common feature in 2 plugins (like wp-admin path name)