If you have a named outline from Fargo 1, you should still be able to edit it and update it and have the results flow through to the web.
In fact, it would be a good idea to open those files now, have a brief look around and then do a Render All Pages from the File menu. This would cause your site to update into the new scheme.
Fargo 2 is close enough to Trex that your sites should render without too many problems. Mine certainly did. (That was one of the goals of Fargo 2's CMS, to run Trex sites.)
I hope Anton doesn't mind, but I saw his blog get updated, and saw it had problems. It's a Fargo 1 named outline, that means it uses features that were in Trex, and not all of them work in Fargo 2, and at least one of them works differently. This is accounting for the not-satisfactory look of his site.
On the Differences from Trex page, we note that the #bootstrapTheme directive changed in Fargo 2. Anton's site is using the old definition. This means that when the page loads in its stylesheet it gets an error, so we're seeing the unadorned text on the page. (Update: I fixed this in Fargo, if you reload the app, and re-render the page, it should look good.)
He's using a feature in menus that isn't implemented in Fargo 2 that was implemented in Trex, the ability to put the text of a page under a menu item. I agree that it's a nice feature, but it's harder to do in a static rendering CMS, so I didn't try to do it in Fargo 2. The answer is to create a top-level About page, and link to it from the menu item. You can see an example of this in the Kim Parker website source.