/u/Khosikulu is the best person to address this question. However, I think he is supposed to writing a proposal right now. I'll give a college-try, though if he reads this he might dispute some aspects, or at least recommend some further literature on the matter.

Did the Dutch enslave the local population, or were they importing slaves from elsewhere, or both? How extensive was the slave population?

In the period of Dutch rule up until 1790s, the majority of the slave population was imported from Mozambique, Madagascar, the Comoros, or else from Indonesia.^1

However, in 1807 the new British administration imposed a ban on overseas imports of slaves to the Cape Colony (as part of an over-all ban on slave trading in all the colonies of the empire). In 1807, the population of the Cape Colony stood at roughly 25,000 white settlers, 1,100 free blacks, and 30,000 slaves.

Was this a plantation style system, plot-farming, or something else?

Slave labor was involved in all aspects of Cape colony society. Slave labor was used in warehouses and as longshoremen in Capetown, as fishermen, and as farm labor growing wheat and making wine in vineyards.

How quickly did things change with the takeover by the British?

So, as I said above, the British imposed a ban on overseas slave imports in 1807. Britain had governed the Cape Colony from 1795-1803 before briefly returning control to the Dutch under the Batavian Republic. When Napoleon invaded the Batavian Republic in 1806, the British again took control of the Cape Colony that same year, and imposed their ban on slave trading the next year.

However, that ban on overseas trade could not completely cut off the flow of new slaves into the colony. Raiding across the frontier and capturing captives, or trading with African traders were also a source for slaves. Of course, the inflows of slaves from these sources were much reduced compared to the overseas trade. While there were roughly 30,000 slaves in 1807, slave numbers increased slightly to 32,046 in 1817, and to 32,243 in 1828. Importantly, this period also saw a shift in the geography of slavery. Some slave owners in Capetown were quick to take advantage of spikes in slave prices immediately after 1807, and sold their slaves to rural farmers. Also, since the eastern frontier was the only viable source for new slaves, the five eastern districts are the regions that see the increase of slave populations, reaching ~20% of total slave population in the colony by 1828.^2

The ban on slave imports also forced the Cape Colony to investigate other labor pools. In 1809, the colony introduced the pass system for contract labor, where free Khoikhoi adults in the colony were required to have passes that specified where the person worked and how long the term of service was. This pass system was introduced as a security measure after Khoikhoi uprisings during the Third Xhosa war.

In 1812, the a system of "apprenticeships" was also introduced, where Khoikhoi and San children were incorporated in the rural workforce. These apprentices were technically free, but they were not paid until they reached maturity at age 25. At maturity, they could theoretically seek alternate employment, but in practice there existed substantial barriers to employment mobility.

Prior to the introduction of the apprenticeship system, Khoikhoi had largely avoided systems of unfree labor, and played an important role in providing livestock in trade to the colony.

In 1834, the British decreed that slavery itself was now illegal in British colonies, including the Cape Colony. Slaves were to undergo 4 years of apprenticeship to prepare them for freedom, and were to fully enter the labor economy by 1838.

To quote Paul Lovejoy

The beginnings of the Great Trek coincided with the emancipation of slaves in the British Empire, and the two were hardly unrelated

....

In the long run, the emancipation of slaves and the further consolidation of the apprentice system [in the Cape Colony] were important steps in the evolution of a migrant labor force, based on the issuance of passes to control settlement and employment. the short term, many Boers took their slaves and Khoikhoi apprentices and moved inland to seize land for livestock and agriculture, for the devastation of the dificane wars had left the best land for settlement. Beyond the British colony, the apprenticeship system functioned as a thinly disguised form of slavery. The Boers who had left by 1837 took with them perhaps 4,000 apprentices and supposedly former slaves who continued to be treated as servile. the Trekkers also continued to seize children or buy them from the rest of the century; the Nguni at Delagoa Bay became one source of "apprentices" were slaves in the eyes of the Nguni. As late as the 1890s, this modified form of slavery continued in the Transvaal, the Orange Free State, and Natal, although by then free migrant labor was more important as a source of manpower than slavery.^3

Emphasis mine.

I think that quote also helps answer your last question. The control of migrant labor and settlement that the pass laws addressed in 1834 would continue to be an animating issue for South African society throughout the 19th and 20th centuries, and labor passes would continue to be used by the Apartheid state.

On the other hand, if we accept Lovejoy's proposition that the Great Trek was connected to the emancipation decree (in addition to Boer perceptions of Anglo discrimination), then 20th century conflicts over land rights and access can be said to be indirectly related to the end(?) of slavery in 1834.

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1 http://www.sahistory.org.za/article/early-cape-slave-trade

2 Transformations in Slavery by Paul Lovejoy, chapter 10 "Slavery in Central, Southern and Eastern Africa in the Nineteenth Century" pp 232.

3 ibid, p232-233