Yep, the only way that I can think of to find biographical and kinship information on the soldier is to get his service record from the UK Ministry of Defence, which costs £30 and yes it requires some downloadable forms to be filled in.
Soldiers had the opportunity to make a will via the military, those wills are available, but he didn't make one.
His next of kin would have been given the opportunity, if their address was known, to submit some brief biographical family details for inclusion on his CWGC record, and if they had done so that information would be listed on his CWGC entry, but they didn't do that, which of course in some cases where an Irish casualty was involved, might be because of the political views of the next of kin in regard to British military service.
However, both of those omissions suggest that his parents might have been deceased by the time of his death.
In WW2 campaign medals for surviving former servicepersons had to be applied for by the serviceperson, medals for deceased servicepersons would have been issued automatically to their next of kin, if their address was known, but if they weren't issued they can be applied for for free from the Army Medals Office by the person's current nearest next of kin.
http://www.britishlegion.org.uk/remembrance/how-the-nation-r...https://www.gov.uk/medals-campaigns-descriptions-and-eligibi...It's a long shot of course, and I don't know if they would release such information to someone who wasn't a proven relative of a casualty, but possibly the Army medals office might tell you if his medals were issued and to whom they were issued.
http://www.britishlegion.org.uk/remembrance/how-the-nation-r...Not hugely likely I would imagine, but you never know, and it costs nothing to ask.
His death certificate can also be obtained for £10 from the UK General Register Office, but it will probably only list his age and not his exact date of birth, but again, you never know for sure.
http://www.gro.gov.uk/gro/content/GRO War Death Army Other Ranks (1939 to 1948)...Patrick Farrell...death year 1945...service number 14400077...rank Rifleman...Regiment Royal Ulster Rifles...Volume 2...Page 48
Where his pre enlistment residence was is of course relevant, but so is his exact date and place of birth, and if you haven't already got his birth certificate, you should get a copy.
https://www.welfare.ie/en/Pages/General-Register-Office.aspxThere are a handful of possible birth registrations for him, none seem to be obviously in Donegal, but I haven't looked too closely, but his parent's details should be enough for the Irish GRO to identify the correct birth record.
Is there definite family knowledge that he died whilst serving in the Army in WW2. ?