Mac app store don't update

Remove "Little Snitch" and test the App Store.

Any third-party software that doesn't install by drag-and-drop into the Applications folder, and uninstall by drag-and-drop to the Trash, is a system modification.

Whenever you remove system modifications, they must be removed completely, and the only way to do that is to use the uninstallation tool, if any, provided by the developers, or to follow their instructions. If the software has been incompletely removed, you may have to re-download or even reinstall it in order to finish the job.

I never install system modifications myself, and (unless otherwise specified in this comment) I don't know how to uninstall them. You'll have to do your own research to find that information.

Here are some general guidelines to get you started. Suppose you want to remove something called “BrickMyMac” (a hypothetical example.) First, consult the product's Help menu, if there is one, for instructions. Finding none there, look on the developer's website, say www.brickmymac.com. (That may not be the actual name of the site; if necessary, search the Web for the product name.) If you don’t find anything on the website or in your search, contact the developer. While you're waiting for a response, download BrickMyMac.dmg and open it. There may be an application in there such as “Uninstall BrickMyMac.” If not, open “BrickMyMac.pkg” and look for an Uninstall button. The uninstaller might also be accessed by clicking the Customize button, if there is one.

Back up all data before making any changes.

You will generally have to restart the computer in order to complete an uninstallation. Until you do that, there may be no effect, or unpredictable effects.

If you can’t remove software in any other way, you’ll have to erase and install OS X. Never install any third-party software unless you're sure you know how to uninstall it; otherwise you may create problems that are very hard to solve.

WARNING: Trying to remove complex system modifications by hunting for files by name often will not work and may make the problem worse. The same goes for "utilities" such as "AppCleaner" and the like that purport to remove software.