Xiaobo -- if you install standard Brackets on your system, are you able to install Brackets extensions there?
I'm assuming you are using the "File > Extension Manager..." menu item to attempt to install the extensions?
today XDK brackets can list available and installed extensions(it is very strange, I didn't do anything), but there is not the JQuery-mobile extension to install in the available list.
Xiaobo -- there is no jQuery Mobile Brackets extension. I think you may be confusing the App Designer UI Frameworks with Brackets code editor extensions. There are seven UI frameworks available for use with App Designer, three of them have been deprecated and will be discontinued in a future release of the XDK. Here's a screenshot:
Is this what you are talking about?
The list of extensions available in the Develop tab is a limited set, we do not allow all Brackets extensions because some interfere with the embedded Brackets in the product. The best solution, if you want a specific Brackets extension, is to do what you are doing, which is to use standalone Brackets to edit your project source files. The XDK has been designed to work with this scenario, that is, in fact, how I use the XDK; I use Sublime and Brackets externally to work on project sources and only use the built-in editor for a few minor things. Works fine that way and allows you to have the XDK open to the Debug or Emulate tab alongside your editor window.
Despite the name, it is not well-suited to the Cordova environment and has not been getting the updates necessary to keep pace with the many changes to the Cordova project. Bootstrap and Framework7 have been staying the most up-to-date and are well-focused on this environment.