SamirGunic
Flagrow is a defunct developer group and the umbrella name for many of @luceos's unaffiliated products and tools for Flarum. Most recently, it was the name of a site similar to extiverse, flagrow.io, which offered a marketplace for Flarum extensions.
Extiverse is Flagrow.io's successor. It's a community-run (by luceos, not affiliated with his role on the Flarum staff or board) marketplace for Flarum extensions. You can use it to browse extensions and find resources on them, as well as subscribe to premium extensions. There may be more features there in the future. Extiverse pulls from the same information that Packagist does, it just looks only for Flarum extensions and Flarum premium extensions that are available directly with Extiverse. It's basically a search engine for Flarum extensions.
Composer is, as you say, the PHP dependency management tool that Flarum uses. It's the main tool for installing/upgrading Flarum, and installing/upgrading/uninstalling extensions. It's independent of Flarum and Extiverse.
Packagist is the repository that composer draws from, so whatever is available through Packagist is also available through composer by default. As I said above, it's a broader library than Extiverse because Extiverse is only looking for Flarum packages, but Packagist is the actual source for the data. So when you use composer, you're actually using it through Packagist, it's just that Extiverse provided you with a direct method of finding the information.
