1. I don't think a new flight can be added to an existing reservation (PNR) without repricing the existing ticket.

2. I don't think Air Lingus and Ryanair interline, so you cannot check bags through regardless of tickets/PNR and you cannot put these flights on the same PNR.

3. I'm confused by the OP's statement now that he (?) doesn't need a transit visa but must apply for a visa. It would help to know the passport and current country of residence (USA?). In most places there are visa service agencies who might or might not (regardless of what they claim) be able to expedite a visa for more money. Moreover, most countries have ways to get a visa more quickly for higher fees, assuming that all documentation is in order, sometimes including proof of travel plans. This would apply to Schengen visas as well as visas for Ireland.