Charles Haine is currently a professor at the Feirstein Graduate School of Cinema.
Since completing his MFA at USC in 2005, Haine has balanced work as a director and an educator. He founded the Academy Award nominated production company Dirty Robber in 2008.
He directed the Feature Film Angels Perch starring Joyce Van Patten and released in 2013. Among Haine's other directing highlights are: a music video for Fitz and the Tantrums "Don't Gotta Work It Out," which featured on Pop Up Video); fashion advertisements for Fais Do Do and Emory K Holiday; and countless book trailers for Simon & Schuster, Penguin, Quirk and many others—including the trailer for Chuck Klosterman’s novel The Visible Man.
You are likely already shooting, but since it's a BMPCCC, you can just shoot raw and have a lot of flexibility to play with color temp in post production.
It does sound like somewhere between daylight and tungsten, letting the window light go a little cool and the interior a little warm, will be the sweet spot.
Since you can't add lighting, that seems like the safest bet.
Full frame? that seems unlikely, such a large sensor. Regardless, you'll see a big savings in file size going H.265, and possibly better video quality. 10bit will give you much better latitude over 8bit.
4k 23.98 as your editing timebase.
60fps in the GoPro for slo-mo if you need it, same with the A73.
I would check the manual, but if the manual doesn't indicate, I'd go for some Phil Wood Grease.
Combines together several cellular hotspots and is a popular choice.
There are even more robust solutions but they get $$$$, this is the one I know people in production have had better results with than just a single phone hotspot.