As D_.. said, περνάω τις εξετάσεις doesn't necessarily mean success (I may have barely passed and I didn't get the marks I was expecting). If you want to say that you have succeeded in the exams you can say Πέτυχα στις εξετάσεις (please notice that you have to put a preposition before the article σε+τις = στις and not use the article alone in this case).
You mean why περνώ τον χρόνο μου = spend my time, uses the verb περνώ;
Well, in Greek if someone says "ξοδεύω τον χρόνο μου" you will understand that he is doing nothing constructive and feel like their time was misused.
Also, to answer your question, different languages use the words differently. I think that "περνώ χρόνο" and "spend time", both make sense if you think about them.