How to make Safari always open in the center of the screen?

The only way to do that is to position the Safari window where you want it to be (location, size) prior to quitting the app. When reopening Safari, that's what you will get (predicated on certain assumptions, one of which is to not close windows when reopening apps — System Settings etc).

Otherwise, don't quit Safari. There is no compelling need to routinely quit apps.

I don’t know that there’s a way to do that, but you can use Mission Control and Spaces.

You can open Safari in full screen in its own space:

View open windows and spaces in Mission Control on Mac - Apple Support

Work in multiple spaces on Mac - Apple Support

It’s also possible to use Split View to tile two apps into one space:

Use apps in Split View on Mac - Apple Support