It’s hard for most people to eat and drink under 1500 calories a day. Are you saying you’re having issues getting up to 1500 calories a day?
Eggs are the cheapest and most perfect protein you can get. Just eat loads of those (around 80 calories an egg) and do some spinach or kale and bell peppers as well. That will cover your veggies and your protein. Then you can fill the rest out with a bit of rice or oatmeal. All of that listed is pretty super cheap.
To your other quaestion- no, you do not need to eat an extra 500 calories if you burn an extra 500 if weight loss is your goal. Eating too little calories (like less than 1200, depending on sex and height) makes your body try to keep your fat and will start removing your muscle in order to make your body have less upkeep. That’s really bad. However, if your body knows it’s getting more calories than that, and that your having to use a lot of your muscles (burning 500 extra calories per day) it will burn off the fat reserves and try to maintain the muscle you keep using.