It would be safest to store it in iTunes.
You can store it in Media Brower also, but if you edit your movie at all, the Media Browser copy gets deleted, because it assumes you will want to re-share your movie. The copy you Shared to iTunes will not be automatically deleted.
When you share to iTunes, a copy is automatically shared with Media Browser.
If you prefer, you can use SHARE/EXPORT MOVIE and name a folder to store your movie.
It is then possible to go to iTunes Preferences and uncheck the box that automatically adds new files to iTunes. You can then drag the movie into iTunes, but it will only have a link to your folder. This is how I do it so I don't end up with multiple copies, and I can see my movies in a single folder.
Yes, once you export your project from iMovie it is rendered and becomes a self contained movie.
You can delete the project and events from iMovie if you wish.
First check whether the movie is available and playable and what size it is.
Look in Username/movies/iMovie Projects then right click on the name of your project and select 'Show Package Contents'.
Then click on the Movies folder to see the exported movie.
In future it is far easier to do this:
iMovie > Share > Export Movie...
You will see a menu that allows you to change the name and asks where you want to save your movie and in which size.
Far easier than Media Browser.