Martin as 6360 served in the 1st Connaught Rangers during the South African War of 1899-1902. It was he rather than Patrick who was wounded at Colenso in December 1899. Martin was invalided home but returned to the fray in 1902 to add the South Africa 1902 clasp to his QSA medal.
John as 5426 served in the 2nd Leinsters during the South African War of 1899-1902.
They all served in WW1 but for none can I find a full set of records. What I can tell you is that John as 294 5th Connaught Rangers suffered a gun shot wound to the head and spent a month in hospital. Martin & William, like Patrick spent most of WW1 as PoWs - all three can be found alongside each other on the same list of PoWs indicating they were taken prisoner in the same action. For Thomas the number 7761 refers to his WW1 service in the Connaught Rangers but 56837 appears to refer to his service in the Northumberland Fusiliers - presumably he was transferred during the war. George who was 25 in 1918 was too young to serve in the South African War but in WW1 was taken prisoner by the Bulgarian Army and was in hospital in November 1918 suffering from Malaria - so probably served in Salonika. Think I have missed out Chris - my rough notes say he was also taken PoW in WW1 but that might be an error on my part.
Suggest, if not already, you sign up to Find My Past & Ancestry - the latter to find Patrick, Martin and John on Medal Rolls. Alternatively a journey the National Archives would suffice but you would probably have to make more effort to find what you want and the travel/accommodation (you would not find everything in a day) would exceed the fees to FMP & Ancestry.
Regards, David.
PS Just realised your listing with regimental numbers was 4 years ago rather than today - so apologies if you have already found all the detail and more, that I have listed above.