Are genetic tests available to detect brca1 and brca2 mutations, and how are they performed?

Yes. Brca1 and 2 mutation analysis is performed at myriad lab in usa. One can either use an oral swab or blood for testing. It is strongly recommended that the testing is done in the context of genetic counseling as the interpretation of the test and risk assessment for breast/ovarian cancer are complex and requires professional explanations.
Yes. But they are expensive and really should be done in conjunction with a genetic counselor since results can be misleading.