Male here - Apparently I need 1800 calories per day?

No.

The important number is not BMR but TDEE. That is Total Daily Energy Expenditure

BMR is what your body burns just by existing. That is keeping your lungs breathing, your heart pumping, your brain and other organs working. You burn it whether you do anything else at all. Although not completely accurate it will serve as a close enough picture, if you were in a coma you would burn your BMR.

The next part of TDEE is NEAT. That is Non Exercise Activity Thermogenisis. Basically the moment you start moving, you will start burning more than your BMR. All those non exercise activities, moving around through the day, cooking meals, doing the various tasks that are part of life all add to your BMR. Even an extremely sedentary person will burn about 1.2 times their BMR just from neat.

The final part of TDEE is EAT, Exercise Activity Thermogenesis. That is the calories you burn that are part of intentional activity.

These three added together will give you your TDEE, and that is what you want to create your deficit off of, not your BMR.

Now to your actually question. You asked if it wouldn't be best to eat as little as possible. At first glance that seems to make sense. The less calories you eat, the bigger your deficit, the faster you will lose weight. However, there is a problem with this.

First, you need a certain amount of nutrients (vitamins and minerals) to remain healthy. To get those you need to eat sufficient calories since nutrients come through food. By eating very little you will create nutritional deficiencies and gradually become more and more malnourished. This is something that is not going to be obvious to you in terms of how you feel until it progresses to the point where it has already done a fair amount of damage. You will find that you will start losing hair, your nails will become brittle, and other things like that. That is part of why you should not eat as little as you can.

Second, your body can only burn off a limited amount of fat in a day. The more fat you have, the more it can burn, but there is still an upper limit even then. Any calorie deficit that goes beyond that limit will be made up not by fat, but by lean body tissue, primarily muscle, but also from other organs as well. That is not a good thing both in terms of losing these things, but also in terms of maintaining the loss later. That lean tissue is more metabolically active, so if you lose it, you burn less calories when you reach your goal making it harder to maintain that weight.

Third, taking that approach of eating as little as you can also messes up your hormones, and the effect is long lasting when the deficit is sever. There as a study with people eating 500 calories a day through the diet phase of 10 weeks. Even a year later the hormones related to weight loss and gain were still messed up.

Fourth, doing this is going to lead to lack of long term compliance to your calorie deficit. In other words, you will fall off the weight loss wagon this way.

All this means that the approach you are considering is not only a bad idea, but a very bad idea. It is pretty much a recipe for failure.

Instead, realize first of all your goal is not simply weight loss but fat loss. To lose fat you should seek to run a moderate deficit from your TDEE. I would suggest using the calorie amount Myfitnesspal gives you when you set your goal to 1 pound per week unless you are very obese then 2 pounds a week would be ok. This moderate deficit will help you lose primarily fat and will help spare lean tissue like muscle. Also realize that Myfitnesspal sets your deficit off of BMR plus NEAT. That means when you exercise you would be taking your deficit from moderate to extreme. That is why you need to eat back the calories you burn exercising. However, in light of the inaccuracies of things like ellipticals with estimate, eating 50-75% of them makes sense.

I hope this helps.