1 - Can I change the max depth which user can nest items?

The default max depth is 5, but you can change that via block controller $maxDepth variable. 


2 - How should I nest/rearrange items?

You should click on 'Move' icon beside item title and drag vertically or horizontally to move or nest items.

3 - How does icon beside page selector work?

The icon beside page selector fetches selected page title and copy it into "Name" field. In case that you haven't selected a page yet, it will simply clear the Name field