One of the things that seemed like a big challenge was getting by with a reasonably nutritious diet without a refrigerator. I grieved that I would have to miss out not only stuff like chilled drinks and icecreams, but also not have access to storing vegetables and meats and dairy products. Further, leftovers would be a liability and likely go waste. However, as I went on, I discovered ways of getting around this, and now, several months down, I have a diet where I am not impacted in any way by not using a refrigerator. As I set about trying to put my discoveries down, I came across another wonderful post on this same topic over here. Here are some of the things I personally discovered along with some of the wisdom already shared in that post.
My challenges were butter, milk, cheese, eggs, stocking up on vegetables for a week or more, green leafy vegetables, stuff like mayo and other dressings, toppings, and other processed pastes, and of course, leftovers.
As I struggled initially with a rice, lentil, and omlet plan, I started out by by adding clarified butter (ghee) to my diet. Ghee does not need refrigeration. Later, I added butter which stays perfectly fine in a covered bowl of water, the water needing to be changed every couple of days. Also, it saves cooking time in most recipes as you dont have to wait for it to reach room temperature. For those not comfortable with the water on the butter (it really is just a drop or two), you can put it in a small wide mouthed jar, and slip the jar into a ziploc bag and put the bag in water.

