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. 

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

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