Yes. The No 16 bus goes from the airport to city center. Use the Dublin Bus route planner to take you from the airport to stop no. 270, and you can see the entire route with every stop.
You can also take the Airlink bus; an express bus, also run by Dublin Bus. Fares are higher, but it is quicker.
Finally, there's Aircoach. They have a regular (every 10 minutes or so) service to city centre for €7.
You would travel first to Dublin city centre, which is only about 8 miles from Dublin airport and from there you could get buses to Castlebar.
There would not be buses direct to it, but all the buses from the airport go to the city centre, and would leave you close to it. You could walk the remaining distance, taking about 15 minutes, or just get a taxi from the city centre. This would be cheaper than getting a taxi direct from the airport.
Yes. There are frequent buses betwee the airport and city centre.
Yes, you can get buses from Dublin Airport to Belfast.
Going direct, the Aircoach route to Leopardstown passes the Belfield Campus. Another option is the 746 bus. Dublin Airport is on the north of the city and Belfield is on the south of the city, on one of the busiest roads out of Dublin. There are a large amount of buses going from the city centre that pass Belfield. So you could get any airport bus that goes to the city and then take one of the many buses that go past Belfield. Check the sites below to get more details.
There is no actual place called the Dublin Exhibition Centre. There are a number of places in Dublin that have exhibitions, most notably the RDS (Royal Dublin Society). Dublin Airport is about 6 miles from the city centre. The RDS is about 2 miles from the city centre, on the opposite side than Dublin Airport. Most of the other places where they have exhibitions are close to the city too. So wherever the place you are referring to is, it is not far from Dublin Airport, within about 12 miles.
The distance from Spain's Bilbao Airport to Bilbao city center is 5.5 miles, or 9 kilometers. Green airport buses depart from the airport arrivals area every 30 minutes for the city center.
Belfast City Airport to Dublin Airport is about 85 miles.
Dublin Airport
There are lots of bus services from Dublin Airport to the city centre.
11 miles. The airport is well serviced by buses running to the City Centre at regular intervals.
At an absolute minimum, you might do it for €20. There are better options, as Dublin Airport is well served by buses which will bring you past Temple Bar for a far cheaper price. They might not bring you to exactly where you are going in Temple Bar, leaving you with a bit of a walk and you might have luggage, but it is a better option.