So here's a problem: I never mapped or storyboarded and got idea in making storyboard only map (I know that's too hard for beginning but still). I found Kite guide, but it contained some elementary stuff, also watched osu! academy, same there. So is there any way to group objects? Because I regularly see maps where different elements move the same way. Also any guides about storyboarding in general would also help.

If you mean grouping objects like group in Adobe Photoshop then in-game editor doesn't has that feature. You have to move thing one by one using design editor. However you can use storyboarding tool like storybrew to move many objects with script. Take a look at its Particles Effect example.