What did Aururians use for currency before the Europeans arrived? What do they use as of the present (in story) time? Does banking exist and what rules govern it?
Aururian currency before European contact was all in the pre-coinage stage.
The most advanced form of currency was that of the Five Rivers. They used a system of clay tokens as receipts for stored food, principally red yams and wattles, held by the temples and (for Tjibarr) the factions. These tokens were then traded amongst people as a form of currency. Unlike coinage, though, the value of the tokens declined over time, based on the expected depreciation of the food in question (red yams were more nutritious immediately but did not last as long as wattleseeds, so lost value more quickly). The tokens could only be redeemed at the place they were issued, and so also declined in value the further they were taken from their origin point.
Despite these restrictions, these tokens facilitated trade quite well within the Five Rivers. They were, of course, largely useless outside of it. With a couple of exceptions such as the Nangu who sometimes accepted tokens issues from port cities, and Durigal where they might be accepted in cross-border trade. They also facilitated some forms of record-keeping and primitive finance for the factions.
Other parts of Aururia used various forms of pre-coinage currency as mediums of exchange, but none of which were as standardised. The Nangu used various forms of what were essentially IOUs to pay their sailors on voyages, but these could not be traded save amongst crews of the same bloodline. Light, valuable goods were often de-facto forms of currency in some areas.
Kunduri was widespread in such usage in the Cider Isle and much of the east coast, and to a lesser degree in Durigal and (unofficially) Tiayal. Salt also served a similar purpose in many regions. Durigal also used possum-skin furs as currency for a while, though that had faded before European contact. In Daluming, stylised bronze weapons were used as a high-value currency. Gold also functioned as a high-value form of currency in Tiayal, mostly in trade amongst nobles (who also tended to be the merchants).
European contact changed Aururian currency dramatically, and quite quickly in some cases. The Atjuntja took up royal-issued gold coinage very rapidly, at first for the purposes of Dutch trade, but then to trade amongst themselves too. (This actually got unstuck because the coinage was so valuable to the Dutch that specie was sucked out of the country very quickly). Tjibarr moved to silver coinage, because they sit on what is probably the largest silver mine in the world at the time at Broken Hill. A lot of this silver gets traded to European companies and the Nuttana and ends up in China, but there is enough silver being mined that even within Tjibarr the money supply is increasing, producing gradual inflation. The Nuttana use gold currency, ostensibly obtaining the gold through trade with the Cider Isle, Durigal and Aotearoa, but in fact they obtain the majority of their gold from domestic sources (Atherton tableland). Durigal has taken up coinage in a more limited way, since they still retain much more of a command economy than other Aururian states.
The Nuttana have developed a strong financial system with record-keeping, profit-sharing and equity rules. It does not operate much like European banking, since they do not operate on the same method of charging interest, but it allows good access to capital and internal and external trade. The Five Rivers (particularly Tjibarr) do have a system of lending and charging interest which is not dissimilar to European banking systems. The Tjibarri system is the most advanced, though oriented mostly along factional lines which affects lending options and interest rates, and with rather a better idea of inflation and how to manage it than most Europeans have grasped. Durigal does not really have a full banking system, though there is extensive record-keeping via the temples and with some small-scale private money-lending.
I suppose it largely depends on whether Dutch colonialism follows a similar path to OTL, in the broad strokes, of a very profitable beginning followed by a massive crash such as what occurred OTL in the late 18th Century. The Dutch hung around in Java in the decades around 1800 largely out of inertia before working out new ways of making money, but those were dependent on tropical agriculture which may or may not be applicable here. Even more though is that this is making assumptions surrounding the Dutch in Europe as well, and that could turn out very different too...
The key question here is when does the easily exploitable gold run out around Kalgoorlie? I say this because at the moment, the Dutch are essentially mining money there, which easily funds everything else. Any other money they get from dyes and spices is just gravy. They have no need to muck about changing things and risk setting off an explosion of revolts / opportunity for other European powers to intrigue and run guns in.
It wouldn't be good to make
too many assumptions about the Dutch in Europe, but it's safe to say that by the *1660s they've become part of the balance of power in Europe. Even the English, who were still fighting wars against them, recognised that have the Dutch be conquered entirely - or even weakened to the point of impotence - is a bad thing in the long run. So while the Dutch may be doing a little better or worse than OTL in terms of European territory and relations, they won't be doing horribly worse.
If I were to make predictions I would say that due to military factors it's very likely that the Dutch retain control over the Atjuntja for a very long time. The European military advantage is still growing at this point and there is no chance for any non-European outside power to take control from the Dutch. Even more, whereas the Javanese were able to largely adopt European technology while large parts of the island (Mataram mostly) remained fully independent the Atjuntja have been "fully" subjugated much more quickly, in that there are no totally independent states in the region. The population crash is also a huge factor, making all the other factors even stronger. Dutch control in 1715 here resembles Java in 1835. Combined with a much more pleasant climate and much lower population density I reckon it's quite likely the Dutch will have an even deeper influence on the society here than in Indo. The introduction of non-Aururian ethnicities will probably have a much more statistically significant impact as well. Whatever society emerges from the Atjuntja will probably be very different from the one that existed in the early 17th century, to a degree greater than most other Aururian polities.
Good analysis.
A few further details I'd add:
European military advantage is mixed when compared to Aururia as a whole. Some Aururian polities are capable of making firearms to match anything which Europeans produce, principally the Five Rivers and Nuttana. Others can and do import European or European-quality firearms, including Durigal and the Dominion. The technology for casting decent artillery is a harder thing to master, though eastern Aururian metallurgy is improving.
The population crash is both good and bad for the Atjuntja. It has taken a severe toll, costing approximately two-thirds of their pre-Houtmanian population. However, it also means that their population will begin to rebound very rapidly starting sometime around 1740-1750. The native population will probably be back to pre-contact levels by 1800-1810. If this is before the gold mines run out of readily accessible gold, then the Dutch will probably still be applying the same management techniques - i.e. leave the nobles mostly alone. This could make things interesting.
Unless Dutch society is totally transformed from OTL, the number of colonists they will be sending out will be relatively few. Aururia is seen as a place where a few Dutch go to get rich and come home, not to settle. Even if the Netherlands has more out-migration than OTL, there are closer and thus safer places for Dutch colonists to travel than distant Aururia (the Cape, the New Netherlands, possibly others). So this is basically a very small Dutch upper class/urban mercantile class. The rest... there will be a significant proportion of slaves/former slaves in the Middle Country too, with the Malagasy being the largest but not the only group. They won't be going away either, and as you note, this is different from most other parts of agricultural Aururia, which are unlikely to see significant immigration.