Aboriginal Australians (is there an accepted shorter term..?)

Aboriginal is generally accepted. It must always be capitalised though to differentiate from the generic aborigine that can refer to the native peoples of any nation.

More commonly used these days (from the 1970's on) they are called Indigenous Australians to be inclusive of Aboriginal Australians as well as Torres Straight Islanders. It is the most politically correct name, though some Indigenous Australians feel it is too generic and removes their identity.

To be most respectful you refer to them by the name of their regional language group; Koori, Noongar etc.

I guess this is a difficult question to answer, in the sense that there are many Aboriginal nations/groups [this map is probably the most comprehensive example] with their own customs and Language.

Also, information on traditional Aboriginal culture can be difficult due to several factors such as: oral tradition and disruption due to colonialisation including the forced removal of children in an attempt to assimilate Aboriginal people into white society [particularly those with paler skin], so information might not be complete or comprehensive.

I'll try to offer some information with a focus on the Noongar [people of South-West Australia]:

Broadly speaking, Aboriginal cultural beliefs are strongly tied to land [or Country]. For Aboriginal people, to have "ownership" of Country means they have a responsibility to care and protect the land, and also to preserve places of spiritual and familial significance. In a sense, they belong to Country, not the other way around.

The name and identity of a place in traditional Noongar culture is more dynamic than Western concepts. As described in Collard, Harben and van den Berg's study of Noongar culture in 2004:

Western cartographic conventions reflect the importance of making boundaries to function as markers to exclude others and demonstrate individual ownership and control. For Nyungar, talking about one place as if it exists in isolation is akin to talking about people as if they exist in isolation from their community. The same place may have many names according to who is using it, for what purpose and at what time of the year. Women and men may have different uses for the same place, or several events may have occurred in a place, resulting in it having several names.

Traditional Noongar beliefs centre around creation stories, otherwise known as Nyitting [ancestral times], or the Dreaming. According to these stories, the Dreaming was a period when spirits emerged from both the Earth and sky to create land forms and the living things that we see today. An example of one of these stories:

At York you can see where the Warkarl (Rainbow Serpent) left a track when he came over the hill. The Warkarl made the rivers, swamps, lakes and waterholes. He came over the hills at York, and his tracks can still be seen. He came down the Avon river to the nanuk (neck) of the river at Guildford, where there is a bend.

When he finished he went to a great underground cave in the river. He did not go on because the water further on was salty. The Warkarl is very important to us Noongar because we believe in the Dreaming.

Elder Ralph Winmar

In Aboriginal communities, the Elders are seen as custodians of knowledge - about Country, custom [katitjin, which includes knowledge of Dreaming stories] and family ties, particularly about kinship groups. All these aspects combined are the basis of laws that govern behaviour and movement within Country - for instance, only certain people/groups of people may allowed to visit certain areas, some may be granted access to places after being granted permission, what resources were to be used at certain times, etc.

Another Noongar Elder, Dorothy Winmar elaborates on this in an oral interview with Collard, Harben and van den Berg [2004], which also further highlights Noongar views of protecting and preserving Country:

They believe in the Waakal very dearly. They reckon without the Waakal around they would have no water. They would not let the kids go and torment the Waakal. They (Nyungar) would drive them away. There is a Waakal in the Swan River and he very rarely shows himself. If the water was muddy, the old grannies used to say don’t swim in there, because he is having a feed. Don’t swim (warra wirrin or bad spirit); wait until the water is clear then you can go and jump in (quop wirrin or good spirit). He was very important to their lives, because they believed in having fresh water. They wanted the water, so they wanted the snake to stay alive.

For additional reading about the Noongar:

Collard, Harben and van den Berg, ‘Nidja Beeliar Boodjar Noonookurt Nyininy,’ Project Report for Murdoch University, 2004, http://wwwmcc.murdoch.edu.au/multimedia/nyungar/info/project.htm

I will probably be Tasmanian-centric in my answer, and given how quickly politics moves, some terms have probably changed, but here goes.

Before European settlement, Indigenous Australia was divided into tribes (there is the trend now towards calling them first nations, as in other western countries- but this is dismissed by some Aboriginals). There were around 600 tribes; Tasmania had/has only 9 of these. There were around 300 languages. There is a tendency to associate Aboriginal Australians with the outback, but the largest numbers were in coastal and river areas. Standard of living was certainly higher in coastal areas.

Tribes numbered as high as 2000, and as low as 100. Groups were small even by contemporary standards- Blainey notes that 'the aboriginal languages ceased to use a distinctive word when they reached the number three' (Triumph of the Nomads). Social structure was familial in nature, with Aboriginal, male, elders at the head. As you would expect with nomadic groups, when members of the tribe were too ill or old to travel, they'd be left behind. Disease was attributed to spells, and usually left to run its course.

Their economy was motivated by hunting and searching for food, with some trade for items with utility but also decorative shells and rocks- some items traveled from what is now Darwin, as far down as Melbourne- there was also trade with Asia, and items from these traders have been found far down south (but there was no contact with Tasmanian Aborigines for around 5 000 years). Tribes did not settle permanently but could spend whole seasons in areas were food was abundant.

Women played a large part in collecting food- diving, hunting, etc. But in Tasmanian tribes, men would eat first. Women carried a lot of the tribes goods when traveling, and fire sticks, and infants on top of this- infanticide was common for a variety of reasons.

Farming was limited largely to things like building catchments for eels; but this is not to say that the Indigenous didn't understand the usefulness of burning large tracts of land to draw out animals, and encourage growth of desirable areas- there was a definite effort to control the environment. Blainey writes that;

Tasmanian hunters, quietly approaching a grassy patch where kangaroos were grazing sometimes tried to surround the kangaroo with a horseshoe of fire, leaving a small gap through which the animals would attempt to escape; at the gap several kangaroos would be easy targets for the weapons of the hunters.

They also understood they could plant seeds, and it is believed they spread yams on mainland Australia.

Food was mostly what the seasons provided, and 'the environment itself was a storehouse' (Lyndall Ryan, The Aboriginal Tasmanians).

As for cosmology I have a limited understanding here, other than they used the stars for story telling, navigation, and as a calendar- sometimes these were connected.