Filter Submenu Dropdown by Search-box

I have some problem here. Please help me and thanks in advanced.
Here the jsfiddle. Questions:

  1. I have search box in my dropdown menu and I also have multiple sub-menu. But the search box only filter on the first dropdown, the sub-menu can’t work. So, how to make the search box can filter the sub-menu and show their parent like this picture?
    Dropdown menu filter

  2. How to make my dropdown menu have scroll bar? I have add overflow: auto in CSS, but my dropdown submenu become invisible.
    Submenu scrollbar

  3. How to make the dropdown submenu always on top? Same the top like its parents.
    Thank you very much. I’m using bootstrap 3.3.5.

Source: html

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