Vielleicht, dieser Sommer gehe ich nach Muenchen fuer studieren!
Vielleicht
gehe ich diese
n Sommer nach München um (dort) zu studieren.
Nur zur Info
When a phrase doesn't start with the subject, it is likely that there is an inversion. See this as other example:
Ich gehe vielleicht diesen Sommer in München studieren. (The phrase starts with the subject, and therefore no inversion)
Is die Klausur or die Pruefung more appropriate?
Don't know, but I'd say Prüfung. Klausur is more likely for exams, but I'm not German, and I think Klausur is typical German.
PS. I didn't mention the "falls" yet, you'll get to that point. But before you do, learn how to name all words in English as well, subject, nominative, accusative, genetive etc. You'll need them in order to use the right article for a word. (e.g. der Mann, des Mannes, dem Mann, den Mann)
Sippy, hilf uns!!!