Lost my Downloads folder both from Dock and Finder
It sounds like when you dragged the downloads folder out of the finder sidebar it vanished before it got to the dock.
if that is correct it is pretty easy to get it back:

Open a Finder window and go to your user folder
In the user folder you should see the downloads folder
Drag the downloads folder to the place you want it in the sidebar
Drag the Downloads folder to the right side of the vertical bar in the Dock

The folder icons in the Finder sidebar and Dock are only pointers to the original. Kind of like Aliases, if you will. Generally OS X will prevent you from deleting the actual folder Downloads along with any of the other top level folders under your user account. But it will not prevent you from removing these aliases in the Dock and sidebar, as you have discovered.
A useful shortcut if you can't find your user folder is Command-Shift-H