1. I don't think of it as "dinner clothes" but the dress code for embarkation day is "smart casual" or whatever they call it now (on the US site they're starting to call the two dress codes "formal" and "gala" but I will not join that party). I don't think it's unusual to wear a blazer and khakis to board, which -- surprise, surprise -- happens to conform to the evening dress code.
If the ship leaves New York on time (5:00PM), you should pass under the bridge before 6:00, and there really isn't much after that worth missing dinner for.
If you're in Grills note that dinner is at the time of your choosing so you shouldn't worry about others waiting if you're not at the table at nominal dinner time. In Britannia they request that you arrive in time to have your order in before 30 minutes after the nominal seating time, e.g., order by 6:30 for the for sitting (6:00 PM). But the first night is a bit of an exception (people arriving late or miss g dinner) since the sailaway fun is happening about the same time as dinner.
2.Will you be in the Grills? Are you interested in (paying for) the behind-the-scenes ship your? Speak to the concierge. If not in grills, I think you queue at the excursions desk before 8:00 AM on the next day. There will be a free ship tour in the schedule on Day 2, but this is just a tour of public spaces so a passenger new to QM2 can learn what's where without having to explore on their own
3. I'm not sure about this one.
4. The Golden Lion serves until 2:00 PM including (usually) on embarkation day. If you're not in Grills its a saner alternative to the buffet.
5. If your booking includes any onboard credit, visit the Purser early in the voyage to verify that the amount you're expecting has been applied. Preferably bring a confirmation from your TA which mentions the expected credit. If there's a discrepancy send an email off to your TA and he/she will coordinate with Cunard. The Purser's office will do the same on their side.
6. If your bring your own wine/champagne or soft drinks that you'll want to chill in your room it's helpful if the minibar contents aren't also in there.
7. Seems to me that we've been aware of the book club in advance although I don't remember how I learned that. I generally haven't seen a book club on the agenda on our annual Caribbean cruises.
8. Only really applicable if you're in Grills...
9. AFAIK a day's notice is sufficient; e.g., mention your dinner request at the previous day's dinner (We don't travel in Grills). There are off-menu items available in Britannia (Caesar salad, shrimp cocktail, fish, chicken breast, steak) but they're always available with no pre-ordering.