I have a separate phpBB forum and I want it to open below the navbar, on the same website, so that it will look like as part of the website, something like that (Image edited with Microsoft Paint):
If you want the phpBB page to have the same look/feel of your site, there are two ways to do it.
1) Build a phpBB 'skin' with the elements you want.
2) Build a custom page template, and put the call to phpBB inside the page area of the template.
Either way is probably a lot of work; phpBB and WP have totally different ways of 'skinning' a page. You might consider a somewhat easier third way:
3) Add your WP theme header image (and maybe some WP site menu links) to the header of the phpBB install with a custom phpBB 'skin'.
I'd also ensure that the phpBB installation is in a totally different folder from any WP folder.
And, you'll need to find a way to integrate a WP login with the phpBB login, passing credentials between both as needed.
A big project (although #3 is easiest, perhaps, if you don't need login credential sharing between phpBB and WP).