Kylie, I assume you have seen this https://teara.govt.nz/en/biographies/3p12/parry-william-edward.
Could Henry Charles be a brother or a cousin, given his age? If so, could he be born in NSW Australia?
There is a will probate mentioned on Archway. Is it on FamilySearch? I can’t see a Military Personnel File in Archway, so I’m unsure if there is an NZ WW1 record as suggested by Marion below.
Possible birth record , in Wales a common place for miners to come to Aus/NZ
Possible WW1 record address is Arch Hill, Auckland
This is the link I found for Joseph and Catherine, not sure it will lead anywhere but you may find some links for Catherine that could be useful.