login and logout behavior issues

Case1: click on the logout link results with the app URL change to “https://nilavema.space/?loggedout=true”. I would expect that the URL should change to “https://nilavema.space/” which is declared as “home”. Am I expected to query URL and somehow issue a redirect to “home” in my own code?

I saw 6 months old question about routing, where you mentioned that you plan to expose “routing events and handlers” (excuse me for not using proper WP terminology – I am a WP novice)

Case2: How do I login to my app, without having to type in the URL “https://nilavema.space/wp-admin”? Is there a login-designer setting that would allow me to request that my app always starts with the login dialog presented to the user?

The page I need help with: [log in to see the link]