The names suggest RC and if that is correct then civil registration only started in 1864 so maybe the date is not correct, or they 'forgot' to register, as often happened close to start of civil 'newly started' registration. If they were not RC then civil registration began in 1845.
Many people had no idea when they were born, migrated etc they made the best guess.
Birthdays were not celebrated like now and on a death cert a birth date/year is not only a secondary 'record' but also hearsay, what other people thought/told and told the authority who wrote out the cert, they didn't have to produce a birth cert to prove what they said, so only gives best guess.
My own Great grandmother had a different birth year on all her primary records, on her grave stone she is written 20 years older than she really was and it is only as I got her baptism record from the parish book that I was able to purchase her birth cert in which the year corresponds and she told the church when she married she was 10 years older than she was, maybe because she was marrying an older man of 23years her senior.
There were many ports they could have left from, not only in Ireland but also in Britain and of course they could have go somewhere else first, like Canada or maybe even across the a European port and then made their way to the US, they often took the cheapest option or the free option ( British Government and Charities paid passages) which may have meant traveling from elsewhere
I searched Griffith's Valuations for Fahey's, hoping they would be located within some specific area of Ireland. This was not the case.
No it is a common name and names alone do not really give you very much. Nor of course does the internet as most Irish records are not online, most are still in the parish churches
You know where John Butler lived before he migrated, I would research from that starting point as he may or may not have been born/baptised there, but it certainly something you could look at.
Also by looking at the 1901/1911 Irish census and seeing if you can find first the family name, then possible family naming patterns ( which the Irish are fond of especially then) and you could also look at occupations and the household. I know they were in the US by then but there will be parents, uncles/aunts, siblings and cousins who remained
