Well, I am italian
and I confirm, the Divine Comedy is incredibly easy to read for me: it is, after all, exactly the same as modern Italian except for some words. Word order is the same, most verbs, while a little unused, are still known.
Latin, on the other hand, has a completely different grammar. I have studied Latin while in High school, and while a lot of words are similar (obviously: Italian derives from Latin), its grammar is a lot more complex, and while you can find the roots of modern Italian grammar in it they aren't really comparable (just as if you try to compare Latin grammar with French grammar).
Modern Italian language has evolved very little after Dante's Divina Commedia. The only other author who influenced the evolution of the language is Alessandro Manzoni with his "I Promessi Sposi" ("The Bethroded" is a close translation): Manzoni wrote it in the same Florence dialect as used by Dante mixed with some words and structures inherited from northern dialects.