Sometimes. It depends on multiple factors.
Yes. Most liver biopsies are performed using the guidance of ultrasound or ct. Most of the time the patient is awake. Sometimes the patient will be given a mild sedative to relax them or to mitigate the pain of the procedure. It is fairly important for the patient to be awake as you may have to hold your breath for a short period of time during the procedure.
Maybe. Most of the time liver biopsies are done under light sedation, which means technically you are not asleep as though you were under general anesthesia. This sedation, however, does make you drowasy and comfortable. It depends on multiple factors though, so you should make that decision with your physician.