To get option (1) working from the management console, it is important to specify the correct extension id and a valid update xml url (not a crx).

One useful feature Google offers that you can use is getting the extension id and the version from the update request.

For instance, you can create a update.php file that outputs an xml file specific to each extension and version. See http://developer.chrome.com/extensions/autoupdate.html under "Advanced Usage".

For more info on packaging an app or extension for managed chromebooks, see https://support.google.com/chrome/a/answer/2714278?hl=en.

Storage Location for Unpacked Extensions

Extension engine does not explicitly change their location or add a reference to its local paths, they are left in the place where there are selected from in all Operating Systems.

Ex: If I load a unpacked Extension from E:\Chrome Extension the unpacked Extension is still in the same location

Storage Location for Packed Extensions

Navigate to chrome://version/ and look for Profile Path, it is your default directory and Extensions Folder is where all the extensions, apps, themes are stored. (If you have several browser profiles set up in Chrome, you will want to view the chrome://version/ page from the profile where the extension is installed.)

Examples

Windows

If my Profile Path is %userprofile%\AppData\Local\Google\Chrome\User Data\Default then my storage directory is:

C:\Users\<Your_User_Name>\AppData\Local\Google\Chrome\User Data\Default\Extensions 

Linux

~/.config/google-chrome/Default/Extensions/

MacOS

~/Library/Application\ Support/Google/Chrome/Default/Extensions

Chromium

~/.config/chromium/Default/Extensions