Hi,
iMovie 10.1.9 (current version) needs High Sierra. Your profile, if it's up to date, shows that you are running Yosemite. If that's accurate you won't be able to update to current iMovie without first upgrading your operating system to High Sierra.
Deleting the app and downloading it again will not cause you to lose your existing libraries and projects, as long as you don't separately delete your libraries when you delete the app itself. Try dragging your iMovie app version into the trash, but don't empty the trash. Leave the libraries alone. Then go to the app store and see if you can download iMovie. It should download the latest version that will run with your operating system. If you want the current version you will need to upgrade to High Sierra. If the attempts to get a successful download fail or can't be done, then you can move your old version of iMovie from the trash and put it back in the applications folder.
Changing Apple I.D's can be problematic. Since you changed your Apple I.D from your original purchase, you might not be able to update. You might be able to purchase current iMovie (for free) at the app store, if you are running High Sierra.
The above being said, it is always a good idea to back up your iMovie libraries to a separate drive formatted Mac OS Extended (Journaled). Formatting or reformatting a drive erases all data on it, so move any data that you want to keep from your drive before formatting.
-- Rich