1) Just because you win far more silver than gold doesn't mean that you got unlucky. In many sports you can win silver without losing a final. In fact only 7 out of the 16 silver medals came in sports where there is a 1 vs. 1 final (taekwondo, judo, fencing, track cycling). Of course you could say that losing 7 out of 7 1 vs. 1 finals is extremely unlikely, but you can't really say much about the actual likelihood of that happening, not every 1 vs. 1 final is 50/50, normally there is one favorite. At the same time you could also say that maybe all those athletes actually were pretty lucky to even reach the final. It doesn't make much sense (in my opinion) to say "Italy should have a better percentage of gold medals, so i am gonna predict a gold medal for them in an event where i actually don't expect them to win gold", instead you should look at all events separately and just ask yourself whether they are more likely than not to win gold in those events.
2) I agree that Italy not winning a single gold medal in fencing and shooting combined is very unlikely. I would expect them to win 3-4 golds in those 2 sports.
3) In his prediction Italy won 8 silver medals for every gold medal, Azerbaijan in 2016 won 7 silver medals and only 1 gold. 6 out of those 7 silver medals came in sports with 1 vs. 1 finals (wrestling, judo, boxing).
Edit: About 1)
If we assume that all the finals with italian athletes are 60/40 in favor of their opponents, then the probability of Italy losing all those finals would be around 3 %.
If we assume that all the finals with italian athletes are 70/30 in favor of their opponents, then the probability of Italy losing all those finals would be around 8 %.
If we assume that all the finals with italian athletes are 80/20 in favor of their opponents, then the probability of Italy losing all those finals would be around 21 %.
If we assume that all the finals with italian athletes are 90/10 in favor of their opponents, then the probability of Italy losing all those finals would be around 48 %.