If there are more than 24h between arrival at ZRH and departure, it's not a "connection". It's a "stopover". So there is a high likelihood that at HKG, your paperwork is being assessed as going to ZRH as your first destination. And if you don't have the rights to enter Schengen, you would be denied boarding.

Regarding 3), your flight ZRH-EWR will likely not be open for check-in while you are still in HKG.

Regarding 4), unsure but unlikely that bags can be checked through ZRH with more than 24h between flights.