William Fegan : Short Biography

I am hoping that someone can help me locate the birth record or parental marriage record for William Fegan who, according to his U.S. Naturalization record was born 1 Apr 1827.  He arrived in New York on 13 Mar 1852 and moved to Newton, Massachusetts. In 1862, he married Mary McLaughlin and had many children.  From here, the record is quite clear, but his history before his marriage is cloudy.

There is a discrepancy in the documents that are key to his existence in Ireland and his parentage. 

First: his death certificate lists his parents as Patrick Fegan and Elizabeth Leahy. Both of these names have a variety of derivations and spellings and I have been able to locate a marriage record in Liverpool for 17 Apr 1817 for Patrick and an Elizabeth Leavy.  There are also some title allotment records in Cavan for Patrick and an eviction notice in 1873 for Elizabeth.  Neither parent has a clear birth or death record.

Second, William's birth dates vary in many census records. I have no real guess as to why this occurs, but they may be incorrect as a result of a transcription error (4 and 7 could have been mistaken).

Third: his most recently discovered naturalization document claims his birthday is 1827 (handwriting is very unclear), but it appears that his county of birth is "Cever" which I have assumed is Cavan.

I am including any documents and images to help solve this mystery.  William is only a great-grandparent away on this direct line to Eugene C. Fegan in Newton, Massachusetts, USA, and it is so disheartening to fail at this point.  

Any help is greatly appreciated!