Meal advice for temporary accommodation:
You need shelf stable foods, including proteins. Canned tuna is great, sardines or mackerel are generally a bit cheaper. Tins of things like white beans or black (puy) lentils can be eaten cold in a salad. Brown rice pouches, again eaten cold (I'm presuming you don't have a microwave). Lentils and brown rice both have good amounts of fibre so are filling.
Eggs can be left out on the side. This sounds gross but you can boil eggs in a kettle- I had to do this when living somewhere without a hob. Put the eggs in, fill up all the way with water, boil, wait 5 minutes, boil again, wait 5 minutes, drain, eat.
Rice noodles, the skinny vermicelli style, can be cooked with boiling water from the kettle. You need a bowl or container with something you can use as a cover (plate, or pan lid). Boil water in the kettle, pour over, cover with lid, wait about 6 minutes and they should be soft and ready to eat.
Iceland sells bags of precooked chicken breast chunks. Defrost and warm by pouring over boiled water, drain, repeat a couple of times. Unfortunately I think they only sell fairly big bags and you'll have to use it all in one go, but could have a chicken feast once a week like this.
You might be able to keep somethings cold in cold water in your sink, like milk. Swap out the water to keep it cool.
Hope this helps a little. I lived without a fridge for ages but had access to a fire for cooking, which made a big difference. You might be able to smuggle in a small electric pressure cooker.