Does the calorie deficit work?

Well, several things to unpack here.

Firstly: technically speaking, all calories might not be the same (differences in energy needed for digestion for example) but these really are details in the sense that:
- there are no calculators to account for that and science really doesn't know enough yet to offer any viable more accurate way to count calorie intake.
- despite this, many people have succeeded in losing weight by counting calories. The principle is that calories in need to be lower than the calories out. Both sides of the equation are just estimates, but by looking at our weight trend we can determine whether or not we need to make adjustments. Adaptability is important, since we're all individuals.

Secondly: needing to eat 6 meals a day is a silly myth, ignore it. Even if it slightly increases meatbolism, it's peanuts compared to your total calorie burn. If you want to increase your metabolism, increasing your activity level and exercise will have a much greater impact. And while burning more calories will allow you to consume more calories, it's not necessary. You can still lose weight when burning fewer calories/not 'increasing your metabolism', you'll just need to eat less.
For a bikini body builder, it can make sense to spread protein intake over 6 meals, but for regular people any meal timing is fine. Just do what feels best for you. To give an example: some people skip breakfast because it makes them hungrier for the rest of the day, other people need to eat breakfast or they binge.

Thirdly, losing weight and maintaining weight loss are both determined by calories in versus calories out (CICO), but many other factors come into play.
- not making things too hard for yourself (don't try to lose weight too fast, don't ban all the foods you like etc.) or you'll end up giving up
- adaptability: adjust your activity level/exercise/calorie intake/meal timing/etc. to find a way that fits for you.
- don't make temporary changes: gradual and permanent changes are more likely to be successful. Not only is it less likely that you'll give up during weight loss, you'll also avoid a common pitfall for maintaining weight weightloss: going back to the way you were eating before your weight loss (and perhaps going back to a lower activity level) and gaining back the pounds.

For your specific case: you speak of a plateau, but a plateau is a longer period where weight loss isn't happening. Which can hardly be the case for you, since you've only been tracking for a month. Weight loss is a rollercoaster. Many people lose a lot of (water) weight the first few weeks of trying to lose weight, and then the body corrects itself and the scale seems to show no progress for a while. Weight fluctuations are an unpleasant reality of weight loss and patience is important. The key is to look past the 'noise' of short term weight fluctuations and look at the long-term trend (at least 4 weeks). Weight loss is rarely linear.
This is my weight loss the last 3 months (in kg). Up and down but clearly a downward trend:

If you give us more info on your situation (your stats and goal) we might be able to give more precise advice.

Calorie deficit is the ONLY thing that works. It is the science between how weight loss happens. Your friend is very wrong, I'm afraid.

As already mentioned on your other thread, you will not lose weight every day or maybe even every week, even if you are keeping a perfect deficit and doing everything right. Weight fluctuates for so many reasons and you need to monitor the trend over a few weeks, not days.