Greetings from Dublin!
With respect, I'll have to offer a little different advice from Gail. You totally can do all the things you mention you want to do in the short window of time you have.
At 10.45 pm, Dublin airport will be like a ghost-town. You'll get through security super-quick unless you have some international arrest warrant looking for you.
You should taxi straight to the airport, Uber in Dublin is dire. The taxi will likely cost €20-25max.
You could bus of course for €7, but your clock is ticking, remember!
Try the Harding Hotel in Fishamble street, close to Temple bar, or any of the hotels in that area. A quick check-in and downstairs to the bar for a nice creamy Guinness and a sing-song with the locals.
All the main bars in Dublin city-centre will be open, and the bars with live music, and all the big pubs in temple bar are open to around 1.30 or 2am. So there no shortage of places to enjoy music and have a Guinness. Temple bar is about 95% tourists, but you aren't exactly devoting enough time to your Ireland visit to be choosy about who you socialise with.
Next morning, over to Trinity college for 9am, into the Book of Kells for an express visit (buy your ticket online in advance and skip the liens). 10am have a peak at nearby Swenys Chemist shop (if you're Joyce fan, then you'll thank you're lucky stars you did) and then to the GPO on foot to visit their 1916 Rising exhibit. But I'd focus on the GPO rather than Swenys, I'm visualising you being young and athletic for some reason so this should be fine and doable, excuse my enthusiasm for such an active itinerary for you if you happen to be the opposite!
Then back to the Harding Hotel, or whichever city-centre hotel you choose. Grab your bag, into the taxi, or bus, and back to the airport for 12.15/12.30. If you have already checked in online and are following Rick Steves advice and only have carry-on, then there is zero reason you should be at Dublin airport 3 hours before a flight. Rightly or wrongly, I believe this is an understandable ploy by Dublin Airport Authority (Government owned) to have you linger among their numerous duty-free shops buying perfumes you don't need and over-priced (and mediocre) coffee.
But, if you like to play it safe in life, follow the advice of Dublin Airport's website and be there 3 hours before your flight. Which means leave central Dublin at 11.30am. In which case you should leave out Swenys chemist shop and just visit the Books of Kells and the GPO (General Post Office).
Alternatively you can get an airport hotel for €100 on arrival, have a pint of Guinness there, fly on next morning refreshed and relaxed... but have no stories to tell anyone back in the land of the free about your action-packed and rollercoaster 12-hour visit to the Emerald Isle.
Keep us all informed of how it goes, many of us will be rooting for you!
Le meas/with respect
Rick Steves Ireland Tour-Guide
Dingle, Derry & Dublin