Register / Login > Profile Menu

I’m currently building a website but would like some help with implementing the Register | Login and Avatar and profile links into the main header menu.

I’ve chosen not to use the wp-admin-bar but instead would like to basically mimic the account logging in/out from it.

I’ve spent a lot of time trying to do this but I’m afraid I’m not quite able to do this.

I’d love to hear from anyone with a solution or ideas.
Thanks in advance,
Brent