I would suggest that Dublin - Cork would be better as a rail journey and the other two as bus journeys. If you look at the map of the rail system on the link above you will see that there are not really good connections between Cork/Galway and Galway/Shannon.
Agree with Doneraile about taking the train to Cork. It's a long journey in the car nevermind the bus with stops along the way,
Dublin - Galway usually takes about 3.5- 4 hours depending on traffic. There is a 5 mins stop at Athlone bus station for a quick facilites break and you can also get some snacks. I would always advise stocking up on snacks to bring with you.
The train is quicker to Galway( not by much) but one nice thing about getting the bus for visitors is you do get to see some of the countryside, and the small villages and towns en route, as well as some of the characters that often get on the bus ;-)
It is also much cheaper then the train!
Galway - Shannon (I'm only guessing here but should be no more then 1.5 hours).
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