Does it work with a public WiFi?
At the far end of a public park the WiFi is very weak, useless. Since I have no control of their WiFi, can I use the extender?
You should be able to, as long as they allow you to access the main router so that you can connect this unit to it. The only thing that may not work for you is if the main router is really far, since this unit has a limit on range. Check the specs to see how far it can effectively operate from the main wifi source (which is probably in the park office).