Egg Shells Down the Garbage Disposal

You could but I wouldn't. With my septic anything that can go in the trash goes there. Also years ago with sewer line I put a bunch of crab shells down the disposal and ended up clogging the drain line and had to open it and snake it out.

Not in our high rise building. The flakes of eggshell do not dissolve at the typical acidity of sewage water and have been known to clog the sewage lines.

IMHO, egg shells and ice cubes are excellent items to run through a kitchen sink garbage disposal, as far as the disposal blades are concerned, but perhaps not great for a septic system if that's what you have. Potatoes and potato peels would be among the worst thing for a garbage disposal.

Yes but I don't. In my first house I had occasional problem so was very caution what went down. It really was a drain problem from the kitchen. Never had a problem after that but it is just as easy to put them into the trash can.

Break up the shells and put some around your tomato plants for the calcium.