QUESTIONS AND ANSWERS

1.    How many members of the Maori Battalion carried the patu into battle ?

To my knowledge none, Maori were very adept at converting their enemies weapon against them and this was noticable during the earlier Land Wars period when they captured or stole British military rifles and bayonets, and used them to very good effect against the British Army.
During the Second World War, Maori soldiers liked the German MP40 submachine gun and there are countless photos of Maori soldiers (and Officers) armed with this very deadly close range weapon.
Another weapon that the Maori also like was the German 9 MM Luger pistol, and dozens of members of the Battalion had taken these pistols either off the bodies of the enemy they killed, or off German Officers that surendered.
Now, the other thing to be aware of, and I have seen this happen many times when I was overseas myself, is that if Maori soldiers find a hard, heavy piece of wood that they can fashion into a traditional weapon, then in their spare time they will set about and carve a traditional weapon, usually a Taiaha, but also I have seen Patu in their "lazy hours," using either a combat knife, or a bayonet.
These traditional weapons are then borrowed by the Unit haka party and appear in all sorts of photos.
However, actually carrying a patu into Battle, I personally know of no recorded instance, but I cannot state this, and perhaps one of my friends might know different.

2.    How many members of the Maori Battalion wore moku's ?

To my knowledge absolutely none. I think the last (male Maori) moko were put on the men during the Waikato War in the 1860's. This was done then to keep the tradition alive. If the men were say 30 years old by that time, then they were probably all gone by about 1930, and the Second World War started in 1939.
The male moko, had become regarded as something of a "War Protest" and after Senior Chiefs like the Maori King, Rewi Maniapoto and others said that they were putting away their weapons of war "forever" then the (male) tradition of moko rapidly died out. By about 1930 it was gone completely.
What Maori soldiers did do in the First World War, and I know this for a fact because I had three uncles in the New Zealand (MAORI) Pioneer Battalion, was this. They were issued with a badge which featured a Maori Warriors head and him doing a "pukana" (rolling eyes, protruding tongue). This warrior was wearing a greenstone necklace about his neck, and it was actually traditional for Maori warriors to go into battle "naked" (however during the Land Wars they wore waist-coats so as to hold their percussion caps). Now in the New Zealand (MAORI) Pioneer Battalion it was traditional for any soldier who had seen action to actually cut out the greenstone necklace and there are many, many examples of the badge cut in this way.

Female Moko:  This tradition "almost" did not die out and the reason for this is because the elders of various tribes had all of their young women who were in the various concert parties for the visiting members of the British Royal family mokoed prior to leaving on their hikoi. Female moko was also considered a very real sign of beauty, especially if the womans lips were completely blue.
As a small boy I was whangaied to my Maori aunt and uncle (I am Pakeha, but half of my whanau are Maori) for the school holidays and at the time my aunt and uncle owned a farm in Te Puna in the Bay of Plenty.
Whenever we went to town (Tauranga) after watching the pictures in Tauranga, we would get fish and chips and gather with the old Kuia (Grand Old Ladies) on the foreshore. They were all mokoed (some chisled and with blue lips) except for my aunty Rama who was senior to all of them. The fact that she was not mokoed was her one regret and she told me this many times. What happened was that her entire concert party got mokoed up in (I think) in 1908 for the visit of the Prince of Wales, however my aunty Rama was a Catholic and the Priest visited her parents and begged them not to let her get tattoed.
I "think" that the last group of Maori women to be tattoed was in about 1910/1912, and as you can appreciate a few of these women lived to a great age and up to the 1970's when the tradition was re-commenced...so the female tradition of moko has never died, and I have several female friends who proudly wear moko.