Never having sailed on the lines you mentioned, I can't compare what they offer to what you'll find on Queen Mary 2. But as for your specific questions:
1. There is so much to do on QM2 that what you must do very much depends on what you want to do. The Insight lectures are always interesting and often outstanding. Afternoon tea in the Queens Room is very popular. If the troupe from RADA (the Royal Academy of Dramatic Arts) is on board, their offerings would be well worth attending. Cocktails in the Commodore Club with piano accompaniment or in the Chart Room with the jazz combo have become musts for us. Walking round the magnificent Promenade deck and, weather permitting, settling in a deck chair as you make your way across the Atlantic is a simple pleasure of which we never tire. Do you like to read? Sitting in a comfortable chair in the library and gazing out over the bow is a must. Even if you don't like to read, sitting in a comfortable chair in the library and gazing out over the bow is a delight. Do you like to dance? There are wonderful balls and QM2 boasts the largest dance floor at sea. And, of course, there are shows, the fitness center, classes, the usual trivia contests, karaoke in the Golden Lion pub, gambling in the casino, and so much more.
2. There are specialty restaurants. The most expensive is the Verandah Steakhouse (lunch $25, dinner $39). In the evening a section of the Kings Court buffet is set aside as a specialty restaurant: Aztec (Mexican), Bamboo (Asian), Coriander (Indian), La Piazza (Italian), and the Smokehouse. The cost is $19.
3. There are several drink packages: soft drinks, soft drinks premium, specialty hot drinks , and a wine, beer and spirits package. They are explained here: https://www.cunard.com/en-us/frequently-asked-questions.life-on-board.faq337.summary. You'll also find information about dining at the same site.
4. I wouldn't stay in Southampton myself, but where you should go once you disembark depends on your interests, how much time you have before you want to be in Dublin, and how you plan to get to Dublin. Winchester and Salisbury both about 25 minutes from Southampton by train. These historic cathedral cities are well worth spending a night or two, and they have excellent rail connections to London (Winchester is more interesting, I think, although Salisbury has Stonehenge). You can travel by train from Winchester or Salisbury to Oxford in about two hours. There are direct trains from Winchester, but you need to change trains at least once if you travel from Salisbury.