A good place to start discovering the Edison's Bluetooth capabilities would be on the Intel® Edison Bluetooth® User Guide.
Now, how exactly do you plan to control your remote car? I mean BLE might not be the best choice for this kind of project, maybe another profile suits the project better.
For your project, I would personally choose the HID profile to control the car from the Android phone, you can learn more about HIDP in section 6.5 of the Intel® Edison Bluetooth® User Guide, but since you are interested in using BLE, I'd suggest you to read section 6.9 since it talks about HID over GATT.
Regarding the data sent to Edison, I believe you could send it using SPP, in that case I'd suggest you to read section 6.7 of the Intel® Edison Bluetooth® User Guide. I have also written a couple of documents about this, you can find them in Intel® Edison User Documents, take a look at them they might interest you.