Yes. Many lab tests are done in a fasting state, however, ca-125 is not affected by eating. Due to variations from lab to lab, it is important to have the test in the same level for follow-up studies.
I believe you can. The lab may have their own protocol, but fed / fasting status shouldn't affect the assay.
Yes. Most blood tests should be done with the patient fasting but eating will not affect this test.