If I keep getting negative tests even after 5 days past my due date, could I be pregnant? (sore nipples, mild cramps, lower back pain, white discharge)

Could be. The best test is a serum pregnancy test. The home tests aren't that reliable, particularly early on. I would recommend seeing your doctor for a serum test.
Yes . Yes. Wait a few days or even a week and check it again. The hormones have to build to a certain level for the test to be positive.