Can we stick the icon inside the board so that they can move together?

@Merve Nama UNSAC - Unfortunately this functionality does not currently exist.

I do see the following Idea in the Wish List section - I would suggest that you add your vote by clicking the blue Votes button: Ability To group items to mind map nodes.

If you have  other ideas, feel free to add them as an Idea in the Wish List section by following the guidelines here: Wish List: Everything You Need to Know.