Do I have to get some blood tests before doing an oophorectomy?

Elective procedures. Elective surgical procedures, like a planned and scheduled oophorectomy, require less blood work than emergency procedures. The type of blood work is usually determined by both your surgeon and anesthesia provider, and depends on your age and other health issues. So answer is, depends on a few things. If you have recent blood work from your primary doc, share it.
Depends. Usually, you should have a ca-125 if there is a suspicion of cancer. Unless you are young, very healthy, and the surgery is at very low risk for bleeding, you will usually need your hemoglobin/hematocrit checked (checks for anemia). You may need blood chemistry and coagulation studies depending on your health status, medications, and complexity of the proposed surgery.
Depends. It depends on why you need the oophorectomy. Generally, you will need a hemoglobin drawn, though this may be done through a fingerprick. Additional tests depend on your health conditions and anticipated surgical bleeding.
Yes, usually. The blood tests you need depend on your overall health. Why does the ovary need to be removed? At a minimum, you probably need to have a hematocrit checked. You might also need to have your blood coagulation checked, as well as other blood tests such as potassium and tests of kidney function. This information will help the anesthesiologist plan the anesthesia that will be safest for you.