Will this work on a Nutone 690 through 696A unit?

Note that Nutone models have sub-models that take different parts. One must be sure of the full model designation, and the parts that will work with that model This (C350BN) replacement assembly works with the 8" X 7-1/4" housing version of the 696N, and not with the 7-1/2" X 7-1/4" Version. The 696-R02 B Model is the smaller size, and so this replacement assembly will not work. One has to use the 690NT (also called just 690) which has both adapter plates, a new grill, the motor and the fan. It is also 60 cfm, and 3 sones (an improvement) See: https://www.amazon.com/Broan-690-Bathroom-Fan-Upgrade/dp/B000NJT45A/ref=sr_1_2?keywords=NUTONE+690NT&qid=1555602608&s=gateway&sr=8-2 (be sure to look farther down the page, as this is a full kit). One can call Nutone at 888-336-6151.

how do I take the old one off?

Just unplug from the built in receptacle. May be a sheet metal screw to take out. Pull that end down, opposite end has tabs. take out and reverse the order to install the new motor. No need to replace the can assuming it's still OK.

Will this work on a NuTone 695 70cfm?

I installed this replacement approximately 10 years ago. I remember that I had a NuTone 695 but I do not remember the cfm. The unit has worked fine all these years although it is somewhat noisy.

The plastic grill is 9" square and says broan. nearly 20 yo, model# indistinguishable. how to remove motor from plate? plate with tabs won't come out?

If you buy this replacement model C350BN. The motor and plate come attached together. On my old unit there was one or two screws that held the old plate/motor assembly into the ductwork portion. Remove the screw(s). I still had problems getting it out because when they plastered the ceiling, they plastered slightly over the plate. I had to break that plaster away to get it to drop out of the ceiling.