My humble opinion: For a transpacific cruise, I would not put any guarantees on there being a usable internet signal for the entire voyage. I would expect there will be times when there is no coverage.
To the best of my knowledge, only HAL regularly schedules priests on their ships to perform mass. Now, it's possible there will be a priest who is a passenger that might offer it, but that's not a guarantee.
#2 is definitely allowed. As long as it is all factory sealed. I don't know if you can bring fresh ginger on. Most people bring candied ginger or tablets.
I'd be thinking the third option would be a no if they contain heating elements.
Yes, but the cruise line will pass the fine on to the passenger.
Again, in the case of a medical debarkation, it's very possible that immigration will waive the fine.