Your only question seems to relate to immigration in Manchester, and as departures to Ireland are considered akin to domestic flights from the UK you will need to go through some sort of passport check in MAN although i don't think you need to complete the UK landing card. In LHR they do a passport check in the FCC when transiting to a Ireland flight.
I would take the direct flight to Dublin and avoid the UK. You could fly from DUB to SNN and then Galway is under an hour drive, or you could take the bus. I would be surprised if the upgrade on the ORD-DUB flight did not clear- what is the I class availability?