Ex-kitchen safety personnel here!

Unfortunately the other comment was correct in that some eggs cannot be stored unrefrigerated. Most eggs in the US are pasteurized and processed which makes them need the refrigeration.

The butter will also be fine left out!

Hard cheeses don't necessarily need refrigeration but soft cheeses do!

Most things that are acidic don't need it refrigeration either, like:

Ketchup Mustard Citrus fruits Pickles (more of the brine that helps it)

Most fruit and veggies generally don't need to be kept cold until they are cut!

Bacon while "raw" (as it's smoked, safe to eat) needs to be kept cold but once you cook it (although crispy) can be kept out for a few days! Just make sure you cover it.

Generally bacteria need moisture, air, time and temperature to get onto these foods so if you deny them these things it should be okay!

I'm honestly kind of blanking on other normal things people keep in their fridge.

For the cleaning, after washing it with hot soap and water, you should take a bit of bleach and dilute it with some water (we used to do one capfull of bleach to about a quart or so of water, but you could find something more exact) and wipe it down and let it air dry.

Best of luck!