I doubt the recorder can do 12x DVD+RW since their is no such thing yet, but I suspect thatâ€™s a typo on your part.
As for the BenQ DR1 I do not know what kind of drive it is but it is probably based on one of the 16xx generation writers (A Russian review of a similar no-name recorder says it's a standard BenQ computer DVD writer with the metal casing removed) but that does not automatically mean you can use BenQ 16xx firmware as the writer is integrated into the recorder as such and I would hazard a guess that it expects a certain firmware revision etc to talk to the DVD writer of course I could be wrong..
To I.D. the drive you would probably need to get a look at the PCB of it and compare it to a picture of the PCB from the 1600 or 1620 even if you were hypothetically speaking to attempt to update the firmware you would need to disconnect the DVD writer from the recorders internal PCB and attach it to your computer in order to flash it with an unsupported firmware.
If I were you I would try and get my money back and get a different DVD recorder one that is better supported by its manufacturer e.g Lite-On 5006 is a pretty good one.