How do you interpret the provided calories over food packages?

Why the sum of them (22+3+5+4) are less than 100g?

Animals are not just made of digestible matter, animals evolved to survive not to be walking candies ready to be eaten at any moment, some of it can't be digested so it is not listed, some of them are micro nutrients and not macro nutrients. Also water weight is important.

Isn't it strange that in 100g chicken filet there is only 22g protein?

What did you expect? The meats with highest protein only have around 24 grams of protein per 100 grams...some types of beans have slightly more, up to 26 grams. And soy has 36 grams of protein per 100 grams of product. If you buy dried soy then it gets to 55 grams of protein per 100 grams of weight. But the same happens to dried meat.

if the provided information is wrong then, how can calculate the amount of fat, protein and carb which i am reeving from it?

You need a laboratory.

To give you a perpespective on what any food with more than 60% protein looks like :

That's protein powder, it is dried food with all water removed and powdered. If you add water again the weight increases and the protein percent decreases.

100 grams of protein powder can be 100% protein. But if you add 300 ml of water then it becomes only 25% of protein when counting the entire weight.

To give you another example, human muscle tissue. Human meat is only 20% protein by weight....the remaining is calcium, salt, sugar, water, iron, hormones like various sterons and other minerals.