Note that the first four listed dishes and their names vary regionally, and are not common throughout the entire country.
But the days when potatoes were the only thing on the menu are long past, and modern Irish cuisine emphasizes fresh local ingredients, simply prepared and presented sometimes with some Mediterranean-style twists. Meat especially lamb, seafood and dairy produce is mostly of an extremely high quality.
Try some gorgeous soda bread, made with buttermilk and leavened with bicarbonate of soda rather than yeast. It is heavy, tasty and almost a meal in itself!
Food is expensive in Ireland, although quality has improved enormously in the last ten years. Most small towns will have a supermarket and many have a weekly farmers' market. The cheapest option for eating out is either fast food or pubs. Many pubs offer a carvery lunch consisting of roasted meat, vegetables and the ubiquitous potatoes, which is usually good value. Selection for vegetarians is limited outside the main cities. The small town of Kinsale near Cork has become internationally famous for its many excellent restaurants, especially fish restaurants. In the northwest of the country Donegal Town is fast becoming the seafood capital of Ireland.
Only basic table manners are considered necessary when eating out, unless you're with company that has a more specific definition of what is appropriate. As a general rule, so long as you don't make a show of yourself by disturbing other diners there's little else to worry about. It's common to see other customers using their mobile phones - this sometimes attracts the odd frown or two but goes largely ignored. If you do need to take a call, keep it short and try not to raise your voice. The only other issue to be concerned about is noise - a baby crying might be forgivable if it's resolved fairly quickly, a contingent of adults laughing very loudly every couple of minutes or continuously talking out loud may attract negative attention. However, these rules are largely ignored in fast-food restaurants, pubs and some more informal restaurants.