Will Mail.app continue to load emails/notifications if minimized by clicking either the red or yellow button (does make difference with red/yellow)?

Mail will receive the emails (and show the notifications) the same way whether you have the window open or closed by clicking on the red or yellow icon.

Emails sent to an @icloud.com address (if you have one) will be received right away because Apple uses push technology to distribute emails. For other email services, the emails will be collected at somewhat random times (your Mac automatically decides when).

You are welcome. The yellow button is to minimize the window, the red to close the window. When it comes to Mail, using either button makes no difference: the window disappears from the screen but Mail is still open in the background.

I didn't want to complicate things. Mail is usually open in a single window but you can open a second Mail window by clicking File > New Viewer Window.

When two windows are opened, the yellow button will minimize it but the window will still exist. You can display it again by clicking Window > [name of the window]. On the other hand, if you click the red button, the window will close and will no longer be available.

The multiple windows functionality comes in handy for other apps such as Pages or Numbers where you can open multiple documents in separate windows.