This is really not a big problem. Except for the fridge (hopefully you get one) what you describe is a full working kitchen. (You will need to wash dishes in 2 dish pans and dump the water-- obviously). Since its summer you might think of bringing a small portable grill with charcol too-- you can have some grilled veggie sandwiches, or veggie burgers one night. Since your fridge situation is not reliable, bring soy milk and tofu in the UHT boxes. You will still need to refrigerate if you use 1/2 box.
This is assuming you will be cooking: I wouldnt rely on finding meat-free food there, so it is safer to plan for cooking for yourself:
Plan out each meal in advance and pack a box of the stuff you need. Each day of the week should get 3 meals and a few snacks. You might not be able to bring much fresh produce, but things like Potatos/onions need only to be kept in a cool dark place like under the counter. Bring a small jar of olive oil-- and in a pan you can make good hash-browns. (dont forget dish washing detergent).
Veggies and fruits: bring the types that dont wilt easily-- carrots, summer squash, eggplant, green beans. Canned flavored tomatos are great for nearly anything. I wouldn't avoid fresh veggies and fruit-- just keep them in a cool dark place or the refrigerator. One weeks worth isnt that much.
Once you make a meal plan, figure out how much you need. Example: you'll need one onion, two large potatos, four apples, 2-3 packs of flavored soy drink, 5 cups of rice, one package of instant oatmeal, etc., Then stick with your meal plan, and you should have just enough food.
Breakfast packaged single serve oatmeal, fruit, and single serve packs of soy milk/ fruit, bagal, peanutbutter. Dry cerial (Kashi is good) and soy milk.
Lunch: Veggie juice, fruit, vegitarian instant soup/ hummas sandwich (fantastic makes dry hummas mix)/ any kind of bean and grain mix. Salad.
Dinner: rice and canned beans or veg chili w/tortillias. Falafal Pitas w cucumbers/tomatos. Pasta w/ maranara sauce and veggies. Garlic bread.