tl;dr: The key to comfort in the air is learning how to fall.
There is no One True Answer to building this sort of confidence. Instead, I'm going to try to give you some specific tips that I've shared with students in class. Some of these suggestions have worked for some of those people: your mileage will vary.
How to be comfortable jumping around?
First, you must learn to fall safely. This front falling video and this side falling video are both excellent illustrations of fundamentals. However, watching them isn't close to sufficient. You must practice falling to the point where your instincts won't lead you to a broken wrist (or worse).
Worst case: if you ever fall over in real life, you might injure yourself less.
Do you practise jumping or flipping on soft mat? Does it help? (I don't got access to these)
I do but that's not the only option. I was the knife wielding attacker in our senior demo team at our local tournament some years ago. We were demonstrating in a high school gymnasium / basketball court. I was flipped and flopped many times during that demo and, while I can't say that the wooden floor was pillowy soft, it was much safer (and more comfortable) than a concrete floor.
Worst case: buy some exercise mats, stack them a couple of layers thick and practice falling at home.
Sometimes when I try jumping from a few steps higher, my landing is really bad.
Add jumping rope and jumping jacks to your daily routine (i.e., hundreds of each per week). Concentrate on landing towards the front of your foot (i.e., less weight impacting on the heel). That's where you'll have the most control over your balance. You'll also strengthen those calves: your landings might not be ninja soft immediately but you'll be able to put your whole leg system to work.
Worst case: Jumping rope is great exercise. Even if you don't turn into a ninja, you'll be more fit.
The same to the legendary 540 spinning kick. My fellows told my to just let my body go, but I just can't.
The 540 kick is very hard.
Full disclosure: I've never managed a clean 540 kick.
If I were coaching you, I would ask that you put that out of your mind an concentrate on achievable goals in the short term. Consider, instead, the tornado kick. Notice how, in that video, the instructors show you all the pieces of the puzzle on the ground. Also, even when everything is running at full speed, they never really get very high. Once you feel confident falling safely, you'll start to feel that that small number of inches off the ground really isn't so daunting.
Once you are approaching mastery of the tornado kick, I wouldn't advise going to the 540 kick directly even though that might seem logical. Instead, start practicing a series of tornado kicks: two in a row, three in a row, etc. Concentrate on the flow so it's not kick - pause - kick - pause but instead is a constant series.
Full disclosure: the combination of repeated tornado kicks is a bane of my existance. As soon as I think I can do N kicks in a row cleanly, I try N+1 and feel like a lumbering elephant.
Victory: if you get to this point, you'll realize that you lost your fear of falling long ago.