When I was living in the suburbs of Asuncion, I got a WiMax based connection to the internet. But that was directional antenna, mounted on a pole that was 5 meters high and fastened to the house.
I could be wrong, but I don't think WiMax was ever intended to make wireless connection over short distances.
For the rest, after you successfully connect to another device (be it by Bluetooth or something else) only the first layer of connection/communication is established. Now the software on the device you use as controller needs to be able to communicate with the software on the device that you want to control. If that is not the case...then the software on either the controller or the controlled can't communicate with the API's both devices have available.
To my limited knowledge software can communicate through an API and options that can be offered to the user depend on the functionality encapsulated in that API. Not all are created equally, so mileage varies a lot. Take a look at the layers in the OSI model, then you will get a more clear picture of what is necessary before software is even able to communicate between devices.