I had this code
particleEffect = new ParticleEffect();
particleEffect.load(Gdx.files.
internal("hdpi/particles/progressbar.p"),
Gdx.files.internal("hdpi/particles/"));
in constructor of public class GameScreen implements Screen. I moved this code into that place, where all assets are loaded ONCE in my app. This resolved both issues. Now it is working on Desktop, and there is no problems with bad rendering of particles.