iMovie

Take a look at this Apple bulletin to make sure that your MacAir satisfies the requirements for upgrading the OS.  

 https://support.apple.com/en-us/HT211683

 In the App store main menu, click on Store and then click on Categories from the drop down menu.   Do your categories then display?  I recall that sometime back, could have been with Sierra, the App store changed its site graphics. design.  

If you ever had iMovie 10 on your computer, even if you deleted it years ago, you still should be able to use the procedure I

previously posted to update and redownload the most current iMovie 10 version that your operating system will run.   I don't think that you can update from iMovie 9.

As for update notifications, have you tried to go to Apple Logo/About this Mac/Software Updates/Advanced and select the box that says Check for Updates?  Try that and see if you get any update notifications.

If nothing seems to be solving your issue, try contacting Apple Support.  The techs there have the capability of remotely accessing your computer that we cannot do here.  Tocontact apple support click on the Contact Support item in the upper right hand corner of this forum’s screen.  Navigate to a place where you can enter your phone number.

-- Rich

Hi, imaalin,

Try this procedure:

To update/redownload iMovie 10, drag your iMovie 10 app from the Applications folder into the trash, but do not empty the

trash. (You can skip that step if you had iMovie 10 on your computer before, but deleted it.) Sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. You will see your purchases displayed, including iMovie 10. Redownload/update iMovie from there. If not successful, drag your present iMovie app out of the trash (if you moved it there) and return it to the Applications folder.

-- Rich

As for the app store Categories being missing, I don't know what is going on there. You should be seeing this: