Is it common for a bipolar person to constantly accuse their mate ofcheating on them, or even just accuse them of things they ddidnt do?

It's not surprising-: -- but it's not a hallmark of bipolar disorder. All "bipolars" are not alike. Like all the rest of us, the individuality of their personalities as well as the particular circumstances of their lives greatly influence their function. They are not "diagnoses"; they are people. That said, those with poorly controlled bipolar tend to be intense & excessive & of course, subject to mood changes.

Yes: When people are struggling with bipolar disorder they often distort information from the environment. This can lead to strange thoughts including paranoia and excessive jealousy.