I measured everything I ate today, and it came down to approximately 1850 calories. Suddenly, I felt hungry again at night. I ate two tiny bags of apple slices (which approximately equals to 80 calories), went down stairs and made cereal (which equals to 400 calories).

I did exercise, but I didn't try as hard so I probably burned approximately 100-200 calories...

I really don't know how to control my hunger? People say that we mistake our thirst for hunger, but even when I drink water, I still have an appetite. What do you recommend?

Can you list what you are eating? That can affect things. Those apple slices and cereal would make me SUPER hungry. I would eat dry chicken breast and perhaps broccoli-not tasty but it would fill me up, or bran. The bran may cause bloat, but cals are cals and it will fill me.
Also, I am scared to say this, because I never read it anywhere but I'll say it-because it is very true for me. I used to be a binger-around 5000 cals a day. When I reduced it to a healthy amount-around 2000 cals, I got hungry. For 1 day-a single day-I ignored the hunger pangs and just slept. The next day, I could eat a healthy amount of cals and did not feel hungry.
If you are a binger, and ate a ton of cals before, I would not be surprised if your body is doing this too-it is expecting a lot of food because it was regularly getting it, but eventually, it will adjust and you will no longer feel the pangs as long as you continue eating a healthy amount.

Do you spread your calories evenly throughout the day? If you are inclined towards nighttime binges maybe saving a certain amount of your budget for late-night snacks would help you control yourself. That way you wouldn't have to completely deny yourself and could 'indulge' within your daily limit. In my experience it can definitely be difficult to stop eating, especially at night, and so I usually just try to distract myself. Going into the kitchen is the first step towards a nighttime binge for me, so I avoid it.

As long as I'm pretty busy, I can ignore hunger pangs that I know aren't really 'hunger'. Maybe I'm thirsty, or bored, but if I know that I have eaten enough filling and healthy food for the day, I shouldn't still be hungry at night. Usually after a few days, maybe a week, of successful avoidance the desire to pig out before bed subsides.

I ate 1 cup of white rice and 2 cups of vegetables. Twice. I don't have a normal breakfast, lunch and dinner meal like everybody does. I wish I could incorporate such a diet in my life, but my family is just like that. Everybody just do their own thing. We eat what we want (explains my obesity). But I'll try and see if I can do something like that tomorrow!

And thanks for sharing that, pixelllate. I'm definitely sure that a lot of people out there do and did the same thing you've done.

If your family doesn't have planned meals, there is no reason why you can't plan your own! Start simple with Breakfast, snack, lunch, snack, dinner, snack. If each one is around 300 calories, you're at 1800 for the day. You can change it depending on your hunger/needs. For example, I like to keep my snacks small and my dinner as my largest meal. It helps me stay on track to plan it that way.

Planning ahead is the only way I can easily stay on plan, so it may help you.

Here is one day in my planning. Just to give you an idea of a full day:

Breakfast: 1 slice ezekiel bread, slice of part-skim cheese, 1 egg white with spinach

Snack: 1 cup blueberries

Lunch: 1 brown rice wrap with lettuce, tomato, mustard, mushroom, roasted peppers

Snack: 4 small carrots with hummus

Dinner: Large mixed salad with chicken, gorgonzola, cucumbers, craisins, walnuts, light dressing

Snack: 2 cups of olive oil popcorn

You aren't getting any protein. OF COURSE YOU ARE HUNGRY, DEAR.

Try to add in some lean meat instead of processed white rice.

2 cups of rice (500 cals) and 4 cups of vegetables should not equal 1850 cals-are you eating anything else? The rice and vegetables will not fill anyone up.
Also, just replace that rice with dry chicken for a couple days and see how that goes-done, easy especially because your family does their own thing with diets.
You will feel full in no time.

You need protein, I agree. Also switch white rice with brown rice. White always makes me hungrier after I eat it. Kinda weird feeling. Like my stomach feels the meal of rice I just ate, but still doesn't feel satisfy. Plain white rice NEVER satisfies me.