how do you put member area's "SIGNUP/LOGIN" button as a sub-menu?

Hi! This is our scenario: We purchased the member area for a specific audience in our site. Now, we don't want to confuse our other audience to see the "login" button that is not intended for them. 

These are the outcomes we want to achieve:

1. creating signup/login button in a sub or drop-down menu to make it subtly visible for specific audience. currently, signup/login button is only visible in the "menu bar". Or if it's possible, creating a button and the pop-up for signup/login will be there.

2. once you login/signup, and you'll be in the private homepage, the logout button will still be visible even if you hide it from the menu bar. currently, we hide our login button and you can't see it in the menu bar. Once we signup/login for testing, I cannot logout because the logout button is not there.

Can you share how to achieve these outcomes? Appreciate your help, thanks.