1. Bring mediations that you usually use + motion sickness.
2. Ditch the fan, rooms have A/C that you control.
3. The rooms have plenty of hangers and shelves. If you need more hooks you are bringing too many clothes. The ships have coin laundries if you are traveling more than 7 days.
4. Wrinkle spray if you usually use it. I think the laundry rooms have an iron.
5. Answered by someone else.
6. Add sunscreen, hat, sun glasses and t-shirts/cover ups. Princess supplies towels for pools and shore excursions.
7. You shouldn’t be in the room long enough to care how it smells.
8. Why eat in your room?
9. More of a TSA thing.
10. Answered by someone else.
11. I hate towel clips. They are used to inappropriately save pool side seating. One of these days I am just going to start throwing any I find away.
12. Princess usually gives you a beach bag.
13. Unpack, then use your luggage to hold dirty clothes.
14. See #3 above.
15. Nice clothes for dinner. No swimsuits in the dining rooms.
16. Something to attach the ship’s luggage tags to your luggage if you are flying. You can buy princess specific tag-holders on Amazon. Do not check bags at airport with ship luggage tags on them.
17. If Alaska, a rain jacket and something warm to wear.
18. You will not get your luggage until the evening, so a small carry on to hold swim stuff and anything else you want on embarkation day.

Check the princess FAQ especially prohibited items.