Navigation and login bar for multisite experience

Hello everyone !

First, I apologize for my English and I will make every effort to be understandable.

I am currently working on the creation of a set of sites via wordpress multisite . Each site has its own subdomain (eg site1.mainsite.com , site2.mainsite.com , etc …) .

I wish all sites in this network have a common navigation bar to switch between the different sites. I also would like to allow users to log in through the bar .

Here’s an example here:

https://www.wowdb.com/

This site is part of the Curse.com network on the left there is a drop down menu with different sites , right menu there is the possibility to log in or register an account .

Is there a login or another way to achieve this ?

Last question: when a user registers on a site of a multisite installation, it can log on other network sites ? I want someone who registered site1.mainsite.com can be registered automatically site2.mainsite.com

Thank you very much for your answers, I hope I was able to explain exactly what I want to do.

Regards.