Your printout wasn't very clear and I couldn't view all the entries, but I was able to search for one name.
I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For William O'Bannon B 1782 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 1 B rcd in 1782 Westmeath. This MAY be for your ancestor. However, at this early date, your chances are very slim - likely less than 10%.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.