Q: Updates won't download and install

Have you checked both of them in your Applications folder to see what versions you have?

You have the current iTunes. You probably have the current iMovie.

Next time you open App Store if those two still appear then try CTRL- or RIGHT-clicking in the description. This should open a context menu in which you can select the option to Ignore/Hide the update.

Then there is a problem with App Store. You might check here: Troubleshooting the Mac App Store. I would also search the forums because this is an old issue.