Leave the Favorite option or Saved Search for users
Regardless of whether you have the user type dropdown enabled or not, you can select what pages to show for user dashboard from theme options.
Note: If no page is selected, all pages will show.
Disable the “Add Listing” Button and Form on the header
Navigate to Theme Options > General > Header and set NO to Show submit property button in header? option:
How to set the theme to save favorites without login
How to make submission free (no membership or paid listing)
To enable free submission navigate to Theme Options > Membership > Membership Settings and set NO to Enable Paid Submission option.
Remove the Register option from header
Go too General -≥ Header Options and set to NO the option to show user login menu in header.