Giulino de Medici's fate, alas, was sealed in history and in the finale. He survives his encounter with Lucrezia's knife which left him floating and looking dead in the water last week, only to be assassinated by the knives of his multiple enemies in the same last scenes that featured Leonardo's last-minute rescue of Lorenzo from a similar fate, prior to the blast through the door. So Guilino dies as history records, but he leaves behind an unborn son, which history also records will become Pope someday.
As I've indicated before, I think this series is at its best when it deals with the real scientific discoveries and inventions of Leonardo, and the dicey politics of this age in Italy. I'm fine when the history is jugged a little, but I find the mythical, magical stuff a distraction, and I hope we'll see less of that next season.
Time travel, however, though likely not scientifically possible because of the paradoxes it engenders - see my Tricky Business of Time Travel - has been a welcome bulwark of science fiction since H. G. Wells. In fact, it's my favorite kind of science fiction, as an author as well as a reader. So I don't mind seeing it all in Da Vinci's Demons, even if it comes as part of the mystical rather than the scientific package.
Leonardo has at least once talked about meeting his older self, and the old guy whose face we finally saw in the Pope's prison last night - I don't know, I thought he called the Pope his brother, but I'm wondering if this somehow isn't an older version of Leonardo? He sort of looks like him ...
We'll no doubt find out more about this in the second season, which I'm very much looking forward to.
See also Da Vinci's Demons: History, Science, and Science Fiction ... Da Vinci's Demons 1.7: Leonardo Under Water with a Twist