Is this forum included in Grav?

Is there a full feature forum plugin available also ?

The forum is provided by Muut.com . There's no forum plugin for Grav (yet) as far as I know.

After signing up for Muut, it's a one-liner to install the forum on your site:

Read the blog post to see how it was done: http://getgrav.org/blog/forum-now-online

Well Muut is quite expensive for a forum, if you want basic functions like private messaging.
Not to mention, when I look at this forum here, it's not very useful for long, extensive discussions over hundreds of posts and multiple pages.

Isn't there any other solution?

I've not really seen anything else that comes close to the ease of integration as Muut. There are other options for forums of course, but usually they require a database and manual integration of users and potentially a custom theme.