It is possible that a person diagnose themselves bipolar?

Possible. In some cases, a patient's symptoms are very clear - such as having a manic episode. In other cases it can be more difficult, such as when a patient presents as depressed but they are really bipolar. It is best to have an evaluation by a mental health professional to get an accurate diagnosis and treatment.
Possibly. But there can be significant overlap between bipolar spectrum disorders and other psychiatric and medical conditions. In general, self -diagnosis my not be accurate. Recommend comprehensive psychiatric/ psychological evaluation. Take care.