So, now I connect my external drive, open iMovie 10, and go to File, and update events and projects?
Yes.
Will the program search for the copied folders or do I have to direct it to my external drive to locate them?
iMovie 10 will search for the copied folders and find them as long as the folders are at the root level of the external drive (i.e, not in any other folder).
Once the program locates the copied files, it should automatically install or create the same projects I had been working on in iMovie 9, is this correct?
Yes. It will create them in a special library that can be accessed from the media sidebar in iMovie 10. Here's a link to the online help menu that explains it:
https://help.apple.com/imovie/mac/10.1/#/mov902ad0c31
Once that is completed I should be able to delete all the movie files from my old computer.
Yes, you can delete the iMovie 9 projects and events folders from your old computer if you are totally sure that you will not be wanting to go back and edit them in iMovie 9 on your old computer. I would keep the iMovie 9 folders that you copied to your external drive. Never hurts. I also would copy the iMovie 9 app itself to your new computer, just in case. Don't delete anything for awhile until you are satisfied that the iMovie projects have updated properly and are working on iMovie 10. Sometimes problems occur.
-- Rich