Hello, Kkerem --
Your Cherokee probably has power brakes. The power brakes are operated by engine vacuum. Since you live in Estonia, it is possible that many of the vehicles you have seen from Russia do not have power brakes.
When you step on the pedel, a valve opens in the power booster and allows engine vacuum to assist your foot in applying pressure to the brake master cylinder. You should not hear a loud WHOOOOSH! but a soft little "swish" sound is not abnormal. Also, the vacuum booster should store enough vacuum for a couple of stops even after you turn off the engine, but it can't hold it forever if the vehicle is not driven regularly.
As the vehicle becomes older, the vacuum booster may become less efficient, and the residual (stored) vacuum could be lost overnight. It should hold vacuum overnight, but I have driven cars that don't. When I first got into the car in the morning the pedel would be roick hard, but the brakes wouldn't work because I was pushing against the booster but not really applying pressure to the brakes. As soon as the engine started, I could feel the pedal fall under my foot when the engine produced vacuum. The brakes always functioned when driving, so I didn't worry about it.
Does any of this sound like it is similar to your problem, or does your pedal stay hard even after you have started the engine?