Is it possible to skip conversation line while playing? By skip I mean for example: conversation is playing (with typewriter effect) and when I'll make input like screen touch on mobile phone or mouse click on PC line will end and go to the next one (by end I mean show whole line)?
Yes. Inspect the Dialogue Manager, and set Display Settings > Subtitle Settings > Continue Button to Optional.
Try this with the example scene in Dialogue System / Examples / Unity UI Examples / Generic Unity UI Example Scene. You'll see a white Continue button. If you want, you can change this button to make it cover the whole screen, and then set the Image's Alpha to zero to make it invisible. This way, the player can click or tap anywhere to continue.
I knew that there is such thing like continue button but your idea with making one big 'background' and invisible button is tricky and it will help me a lot.
