I assume it is legal to walk a bike on the sidewalk, Is it legal to walk (push) a car on one?
Also I know is it is illegal to drive on the shoulder, but what about on the grass to the right of the shoulder?
NY laws apply.
Sidewalk 3’ wide. Car 6’ wide. Trees planted on either side of sidewalk. Pushing the car on the sidewalk violates the law. The law of physics that is, no two objects can occupy the same place at the same time. 
Other than that I got nothing
I guess Rick you have never drove in a big city where you sometimes have to drive in the sidewalk to get out of a parking spot that a double parker has blocked you into.
In many cities, it is illegal to ride a bicycle on the sidewalk. You will be ticketed and fined here in Chicago.
It is also, I hope I need not add, illegeal to drive a car on those same sidewalks.
I got nothing useful to add to this thread, but it did remind me of a story…
About 10 years ago, I went to Vegas with some buddies… cabbie that picked us up was crazy… it was New Years, so the Strip was crazy packed with cars… anyway, our hotel was across the street, and since traffic was so bad the cabbie drove down the median and cut over. This was before there were palm trees lining the Strip.
I paid the guy $50… = )