Yes, you can use the SOAP (WSDL), REST (JSON), HTTP Get o HTTP Post. for more information Documentation
The current limit is 25.000 request per day and per device.
The request can be combined, i.e. you have 4 devices, you can make 100.000 requests daily, does not matter the device's source. If you needs more requests you can buy more devices API.
Yes, your desktop App can connect from exposed APIs