In ww2 a "Maori Battalion" was formed and served with distinction in North Africa and Italy . http://www.28maoribattalion.org.nz/

I can't say about aboriginal troops; but yes there were Maori troops in the world wars. My knowledge is mostly of the First World War though.

Sir Peter Buck (Te Rangi Hiroa); was one of the earliest Maori members of the New Zealand parliament; he was educated and had served as a medical officer in Maori communities before taking office. When the Great War began he recruited a number of Maoris to support the British war effort and volunteer to fight in the foreign theater (Europe). Te Rangi Hiroa did not just sign people up to go fight though, he went with them and served at Gallipoli (earning the Distinguished Service Order at the battle) with the "Native Contingent" as the Maori troops were refereed to at that time.

Not all Maori supported the war effort- 1914 is only a generation on from the series of wars fought between the British Empire and the Maori; and the war was fought on a foreign continent far from Aotearoa (New Zealand), so it was hard to feel a lot of loyalty to the British and to the war effort. By the time of mandatory conscription in 1917, there were a number of Maori who chose imprisonment rather than serve in the armed forced of the British.

So short answer; Yes they did fight, but it was in the "Native Contingent" later the "Maori Pioneer Battalion", they did fight with ANZAC regiments at Gallipoli, but were largely kept separate and distinct from the 'white' units of the empire.

Reginald Walter Saunders. The first ever Aboriginal officer fought in WWII in the Africa, Crete and New Guinea campaigns.

Source: http://www.awm.gov.au/blog/2009/02/13/reginald-saunders/

There was a Maori battalion which fought as part of the 2nd New Zealand Division in WWII. I know they fought at Monte Cassino and got in a bad spot (which happened to a lot of troops in that battle).

This page has photographs of Maori troops performing a haka (war dance) in WWI and WWII.

Yes on both accounts. /u/b1uepenguin has done a great job of talking about Maori experiences so I'll tackle the indigenous Australian aspect. This is unfortunately a very tragic part of Australian history and one that is often overlooked even on Anzac Day. More then 1000 aboriginal Australians volunteered for the First AIF during the First World War. Initially government policy prevented them from doing so on the grounds of race but there were ways around this such as claiming they were pacific islanders and even Maori's who for whatever reason were held in higher regard then indigenous Australians were. As casualties mounted and the pool of volunteers began drying up, restrictions were relaxed and the government ordered that "Half-castes may be enlisted in the Australian Imperial Force provided that the examining Medical Officers are satisfied that one of the parents is of European origin." There is some debate around why aboriginal Australians chose to enlist, there are claims that it was a desire to prove themselves as equals, to travel and see the world but I think the most compelling argument is the promise of 6 shillings a day which was more then they could have earned in Australia.

While serving, indigenous Australians generally found themselves to be accepted as equals and there was hope that this would translate into civilian life. This was tragically not the case and indigenous veterans returned to an Australia that still discriminated against them despite their service. Soldiers returned to find their children had been taken by authorities while they were gone and they were excluded from the Soldier Settlement Scheme set up by the government post war. Even more tragically, much of the land that was allocated by the government for this scheme was taken from Aboriginal Reserves, forcing the inhabitants to move further away from their traditional lands and the places they had come to call home.

The interwar period saw tighter control by the government of indigenous affairs and as late as 1928 aboriginal Australians were still falling victims to 'reprisal massacres." Political movements to better civil rights of Australia's indigenous populations largely failed.

During the Second World War, aboriginal Australians enlisted again and served throughout North Africa, the Pacific and the Mediterranean, with the promise of full citizenship. Reg Saunders, an indigenous servicemen in the army, became the first commissioned aboriginal officer. Perhaps more critically important is the involvement of Australia's indigenous peoples on the home front. Aboriginal men and women served with the auxiliary service as well as the war industries and were granted many freedoms they had not known before. Unfortunately it would be another 50 years or so before full citizenship status would be granted to them.

Sources:

Australian War Memorial website

A Military History of Australia by Jeffrey Grey

Defending Whose Country? Indigenous Soldiers in the Pacific War by Noah Riseman

Australians at War by A. K. MacDougall