How did they get rid of the waste?

You have to remember Calvin was a genius, albeit loony. I'm sure he prepped for every scenario imaginable to the point of insanity.

For the air part I'm sure he built a complex air system. I seen many docs online promoting you need to both make sure you have a solid vent for the air and make sure the cracks are covered. The vent converts the air to being clean and eliminates the half life and radiation plus it helps control the temperature. Calvin just put it through the septic line which is smart because it's not close to the surface. Plus covering the cracks prevents excess radiation coming in. I'm sure the locks helped with that.

As for the food Calvin had a little bit of everything. Meats I believe he had a lot pounds worth of beef, chicken, turkey and ham stored and frozen. He had the fish in the tank and I'm sure he allowed them to constantly repopulate. He had all those different cans and made it look like a grocery store with the cart. He had a lot of boxes in that setup too. Then he had that garden where he grew plants and other things, sure he grew veggies there. I'm sure had syrup to make Dr pepper and other soda. He probably had boxes of pasta and army rations in worst case scenarios.

He also had a lot of home improvement stuff like the ceiling items for instance.

His only real downside was the lack of a working radio (that was just idiotic in the long run, he could have radioed for help possibly if he had the right equipment,) lack of any quality entertainment (he could get honeymoorners but no other TV shows, newsclips, or films. But he has all kinds of records,) and anything for the wife to do or use. No wonder she got miserable.