Is there any advantage to setting my thermostat fan to "ON" so the fan runs constantly?
Most experts agree that you should set the thermostat on the "auto" setting and let the A/C unit do its job. You will see little, if any at all, noticeable difference and consume excess energy leaving the fan in the "on" position while running the A/C. 

How close to the outdoor unit should I plant shrubs or flowers?
Manufacturers generally agree that plants should not be closer than 18 inches. Air conditioners need to take in and exhaust air to operate efficiently. If air cannot circulate, the unit could build up heat and require service.

How often should I change or clean my filters? 
Filters should generally be replaced every month when the system is running. Replace filters with the same kind and size as original filter. If your filter is not disposable, follow the manufacturer instructions for cleaning.