Boarding a ship right before Shabbat was an issue in the old days, because then you ended up seasick on Shabbat. Nowadays the ships are made very well and you don’t automatically get seasick. It does happen, but we cannot guess which day it will happen.
2,000 Amot is correct. Since Techum is Derabanan, you can count the measurement of an Amah as 2 feet like the Chazon Ish.
2,000 Amot equals 4,000 feet. That’s the radius from when you leave the ship.
Correct. You cannot carry unless there’s an Eiruv.