Yes, if you request, the wait staff will sing happy birthday and provide the birthday girl or boy with a cake. When in doubt, you can ask the Head waiter/ Maitre D'.
When I was in St. Martin I went to Orient Beach:
It was really beautiful, and worth the long, bumpy ride in a van to get there.
Be warned that you will encounter nude sunbathers on the south end of the beach. But you will be severly dissappointed if you expect to see something nice; as almost all of the nude sunbathers I saw were at least 65 years old or older.
If you are into shoping St. Martin (Maarten) is a great island for that. I hear the best shopping is in downtown Phillipsburg, near the cruiseship dock.
As for shore excursions, I did not have any shore excursion when I was there. I went to Orient Beach instead. However, I heard good things about a shore excursion onboard a Catamarand sailing around the island. I heard good things about a shorex. involving a trip to a butterfly farm in Margot.
I was also in San Juan in 2007. I went on the shorex. titled "Walking Tour of Old San Juan". This shore excursion is for people fascinated with old buildings and places that have been around for 400+ years. It is not for people who can only walk short distances or people who can not walk up LOTS of stairs or uphill.
Another San Juan shore ex. I heard was really good, was the tour of the Bacardi Rum factory.
I never been to Labadee. I heard it is a private resort only for the Royal Caribbean cruise passengers.
I hope this was some help.
Have a great time on your cruise