Missed period. Discharge and no period?

My girl friend (22 years old) has irregular periods and last period comes on july 4 to 7(more than 40 days delayed and I think 46th day(not sure) the period comes on july 4  to july 7) july 8-july 11 in these days we had protected sex. August month periods are missed till now. August 27-August 29 in these days we had protected sex. In September she had cramps for limited time and white discharge also comes 2days happened like this. we think that periods will be coming but no period comes. And September 10 take home pregnancy test and result is negative. (August 29 to September 10 is the 12th day after protected intercourse we administer a test and result is negative) In Septembe some of days (6,7..18,19) she had cramps and white discharge came.  Is she is pregnant or not? When will take home pregnancy test next? Why the cramps feeling and white discharge and no period? July 4 to 7 is the last period date. After that till now 75 days no periods came