Not significantly. Fluoxetine blocks an enzyme at the liver that breaks down some medications. Most anesthetic medications are either not metabolized at all-- the inhaled agents-- or are broken down by several mechanisms. Fluoxetine does not affect hemodynamics or other life functions in a way that would interfere with anesthesia.
No. Prozac (fluoxetine) does increases levels of serotonin, a neurotransmitter; narcotics do also. If too many drugs are given which increase serotonin, a serious complication- serotonin syndrome, can occur. But this would be very unusual at normal doses. Your anesthesia provider should however always know about all the drugs you are taking, including over the counter and herbal supplements.
No. No worries here, the ssri medications are safe to take up until the day of and can be immediately continued.