fvila hello and welcome !
fvila a description of the purpose of the site
You should have seen a banner that serves just that purpose. Once dismissed it doesn't come back though. If it doesn't fit your needs there's plenty of ways to extend the homepage through custom CSS or an extension.
fvila a list of the categories (or forums, or subjects, or whatever)
In Flarum, those are called tags. Tags behave like categories or (sub-)forums in most other softwares. This should explain why tags probably aren't your typical expectations of tags.
One big difference is that a discussion can have multiple tags at once (you can configure that in Flarum admin settings), hence the naming. There are also primary and secondary tags. The best is to play around with them on a test forum to understand how they can be used 😉
Traditional tags (we could call them hashtags maybe ? It sure is a bit confusing) could be added via another extension. I don't think anybody made such an extension yet.
fvila with a description of each and a few statistics on the usage
You can access the Tags page from the homepage. There you find descriptions for each tags and some other information. For a "classical" forum layout you can have a look at the Koseki extension by Reflar Koseki also adds additional stats like discussion count.
fvila One thing that might limit the usefulness of the color coding would be for color-blind people.
Feel free to set your own colors, use custom CSS or an extension to improve accessibility. You can even contribute back to the forum if you find something to improve in the core software !
fvila Once the forum is selected I don't think you need to see the list all the time
What list are you talking about ? The sidebar with the list of tags is only visible on the homepage as far as I know. Do you mean hiding the list of tags once a tag is selected ? Unless you have something else to put in the sidebar I think it's nice to keep it.
The best thing about Flarum is its extensibility. All the things you mentioned can be changed via an extension if needed. If you're not into coding it could be a bit challenging but you can find many great developers here if needed. And Flarum is already great even without any custom extension, don't hesitate to give it a try !