You always want to pull air out, that is an "exhaust fan" and will always make for better circulation. When the fan is pulling air out of a space, it is creating a vacuum and will allow air to be sucked in (from somewhere, more later). Pushing air in will only pressurize the space not allowing the hot air to evacuate the space as quickly thus slowly heating up the space that you are trying to cool.
That is incorrect. The same somewhere that can suck air in can also blow it out. It's all about temperature difference and volume.
Push-pull is always better but if you have to choose one try to complement natural air flow. If you have a natural breeze blowing
in the window you don't need an intake fan there, use an exhaust fan instead far from the intake window (second window, doorway).