How to uninstall a program through the App Store?

No.

You cannot uninstall apps from within the App Store.

How can I delete an application?

1. You can delete them like in iOS:

   • Open Launchpad.
   • Click and hold the app you want to delete (or hold ⌥)
   • Delete by clicking on the X.

   Note: The X appears only for apps which have been installed using the Mac App Store.

2. Locate the Applications folder where the app is located:

   • /Applications or /Users/my_name/Applications
   • Drag the application to the Trash.

   Note: This will only remove the application - this will not remove some other files which may be related to the app (e.g. preferences). If you want to remove such files as well, you can use tools like AppCleaner which @james.garriss has mentioned.

Besides this, applications which have not been installed via the Mac App Store sometimes provide their own uninstaller in the installer .dmg image. I usually keep them in a folder Applications/Uninstaller which I created.

Yes, it is possible under macOS Catalina. Not sure when this became available. When in App Store, click on your account in the bottom left corner, the list of the apps installed under the account will show up. Move the cursor over the app which you want to remove; a round button with three dots on it will show up next to it. When you click that button, a drop-down menu opens where you can select to remove the app.

I recommend using AppCleaner from FreeMacSoft. You simply drag-and-drop the application you want to uninstall from your Application folder onto AppCleaner. It does the rest, including finding and deleting other related files on your system.