Really any kind of sites?

Hello!
My main cms - Joomla. I'm using it more than 10 years.
I found Grav and I want to try it.
Is it really to build any kind of sites?
Is it possible to use extra fields and filtering in frontend, like E-Commerce sites?
Is it possible to create forum with Grav?
Is it possible to create files downloads site with counter for each file?
I just can't imagine how it possible without database.
Thanks.

Yes to all of the above, though not out of the box. Fields, filtering, sorting, and handling many items for an eCommerce-site isn't all that difficult - you'll accomplish all that with Twig or JavaScript. You'll need a payment-operator though, but there are at least two plugins which can provide this.

There is not an integrated forum-plugin, but there are OAuth- and LDAP-plugins which you can use to authenticate with both Grav and most modern forum-solutions, and they can run alongside each other without issue.

You can create download-counters, but there are no built-in solutions that I'm aware of, so you'll likely have to code it yourself.

The traditional database is just a storage-layer working with the CMS. There's nothing in a storage-layer that cannot be accomplished using files, key-value stores, or any other type of storage as long as it can receive and give back data that the CMS can use.

For heavy-use sites, or intensive operations like large eCommerce sites or popular forums, I'd want to go beyond flat files regardless - and also invest in more extensive caching, load-balancing, routing and asset-handling. Grav can still be the presentation-layer, like pretty much any CMS, it will just require less resources than most.

Is the current forum builded with Grav or it's 3-rd party engine?

It's based on https://discourse.org, rather sofisticate and complex discussion software.