"Can I insert an old distributor shaft attached to an electric drill to prime the pump?"
No
"Would it be possible to fill the crankcase by pumping break in oil through the sending unit port? Thanks."
Yes, this can work. Screw a hose barb fitting into this location and then fill with either a gravity fill, pressurized tank full of oil or an external oil pump in a bucket of oil. I've done the last by fabricating a plate and nipple bolted onto the outlet of a SBC oil pump. The pump is submersed in a 5 gallon bucket of oil, clamped to the bucket and running the hose to the sending port. I used an air drill with a tool like this, https://www.jegs.com/i/JEGS/555/23640/10002/-1, that engages the pump, as the bottom of a SBC distributor does, and primed it.
Glenn