1) Not if it's a screw cap (hah!) but many people do take a travel corkscrew with them
2) Any of those
3) Yes, no issues with the new menus
4) They'll be pre-loaded onto your card and a list describing them in your stateroom when you board.
When our son was young, he would only drink milk on a ship along with other dairy like yogurt. Wouldn't eat anything else (as hard as we tried, and as hard as the crew tried).
But we still ate in the MDR and it wasn't a big deal. I wouldn't let your son's penchant for milk stop you from at least trying the MDR.
No worse than people who have checked in but walk up to the counter without any of their documents out and are fumbling through their bags to find them.
I haven't been on Voyager, but Voyager matches Navigator. I didn't think Navigator's suite lounge was small.
I've never seen the suite lounge full on any cruise except for the first night and sometimes the last night. At least since they moved the lounges out of the windowless midship area.
Neither of those are exclusive to a cruise line. They may have their own twist on them, but the tiramisu martini and kiss the lips are public domain cocktails