Minimize and close out button disappears in full screen mode

That is what Fullscreen means. You can make them appear by moving your cursor all the way up, at any time.

If that does not work for you, then do as dialabrain suggests and just maximize your window, without going to fullscreen.

This can also be achieved by option-clicking (rather than just clicking) the green button.

You would have to "zoom" the screen instead of switching to Full Screen.

You can't, that's a design feature. However, all you have to do is position the pointer to extreme top of the screen to reveal them.