Those airplane bathrooms are really difficult. You have to depress the taps. If you are alone, this will not be an easy task!
For such a long flight, I would switch over to a system with disposable liners. I know Playtex and Avent have them, maybe some others. For such a long trip, it's worth changing bottle systems. You'll also find it easier when you're out and about.
To make your trip easier, fill up the bags ahead of time with the amount of formula you need, roll them up and put them in a ziplock. Then you only have to add the water. This is much easier than jiggling individual packets or those clumsy separator tubs.
I did wash the nipple and ring on the plane. You can ask for some hot water to do a final rinse in a cup. No, there is NOT always a sign in the bathroom saying not to drink the water. On some flights, especially short hops, you might find them but on long-haul international, the water, in theory is drinkable.
I'm living proof that it is lol! In my years as a Flight Attendant, I never had any problems with crews or passengers with the water on board. Maybe my airlines were super-careful? Go with bottled if you prefer and/or talk to your ped.
Make sure your baby takes his/her bottle at room temperature. A warm bottle has no health advantage and is a real pain to do when traveling.
Do NOT depend on the airline to supply you with endless bottled water. You need to anticipate how much you'll need. We barely had enough for the first meal service and then it was the filtered tap on board.