How Do I remain in Active Desktop When Opening another app?

When you run an app in full screen mode, it essentially has its own desktop, so if you call another application, that second application will open on another desktop. Basically, if one application is run in full screen mode, it's not possible to run another application on top of it on the same desktop.

If you use multiple desktops (Spaces), and have assigned Mail and every other app, incl. Safari to different desktops (Spaces), and all of these applications are running, you can half-way do what I think you want to do...

System Preferences > Mission Control, uncheck 'When switching to an application, switch to a Space for the application.'

Now, when you are in Safari (not full screen), and you click on the Mail icon in the Dock, you can stay in Safari's Space and keep your Safari window viewable, but you'll also have Mail's menus available in the menu bar at the top of your screen. If you choose an item from one of Mail's menus, or if you click on its Dock icon a second time, you will move to Mail in its own Space. If you click in Safari's window, the menu bar will again show Safari's menus.

Also, if Mail and Safari are both running full screen, then you are just a four-finger swipe away from moving back and forth between them at will, keeping both in front at the same time in each of their separate Spaces