Can I accept offers from universities in other countries before I apply to a German university?
I doubt that the German university somehow knows that you are enrolled at other foreign universities, but it's generally forbidden to be enrolled at two German universities at the same time. However, it is possible and legal to enlist as guest student ("Zweithörer" or "Gasthörer" in German) while enlisted as full student at another German university. This might apply to non-german universities as well.

Regarding the application deadline: as far as I know the deadlines for normal applications is mid-july for the winter semester and mid-january for the summer semster. Normally, you get the results within 2-3 months.