CMD + Tab from fullscreen app switches to wrong application

You can configure these shortcuts in System Preferences -> Keyboard -> Keyboard Shortcuts -> Mission Control

I think the default is control-option-left/right arrow, at least that's what I have it set to.

In mission control, you can also re-order the position of the desktops/full screen apps by dragging them around. I think by default they're ordered by most-recently used desktop, but you can change that (I can't remember how, that would be a separate question anyway).

If you hold command and quickly tap tab you will cycle between your two most recently used applications without bringing up the heads up display.

If you want to use a third party app Witch has options to ignore minimized windows.