BMPCC 4K Recording options

Is it possible to record Prores HQ to the SD card and RAW onto the external hard drive via the USB 3.1 at the same time?

Not likely, you are asking the camera to process parallel two different data rates and codecs at the same time. I think this will be beyond the camera’s ability. Even the Ursa Mini Pro can not do this.
Cheers

Denny, you mean to say that only one of the three options will be active during recording? So if I were to record HD prores on SD and 4K prores via USB3.1 it will not be possible.

No, only one recording option is available at any one time, no parallel recording to media, not even the same resolution setting. BM cameras can only record in resolution at a time, each time to reset the resolution, the camera does a soft reboot to change the setting on the video processor. To do what you are asking would require two video processors, each with their own recording media slot.
Cheers