Firstly, colonisers weren't there to bring enlightenment. There were there to exploit the natural resources and the population into sending monetary wealth and material goods back to the homeland. Every institution established by the colonisers were meant to continue the tradition of exploitation and if the inhabitants got some secondary benefit out of it, then it was of no concern to them or could be used to further exploit the colony.
Thus the adoption of say, English, was done through the school system where the British would need local people to do the work which they could not do. For example, many of the governors of British Indian provinces and higher levels were predominantly British, while those, such as Tax collectors, and lower levels were local Indian subjects who went through the newly established British school system who were trained for these positions with the added benefit that they could speak both the local language and English and could be trusted to do their jobs. Hence why you see such disparity among British Indian subjects on who would actually go into academia, such as the nobility or those with means, and rather rarely others who the British were mostly content to work menial governmental jobs for a megre salary.
Religion, however, was a different ball game. You see the spread of Christianity more effectively among those who were not part of the Abrahamic faith or were not that numerically numerous such as those who believed in Hinduism. A colony in Africa, for example, would be much easier to convert because you could militarily dominate them, should the need arise, and because they didn't have a solid base to resist preachers. In India and elsewhere it was much harder and continued to be a problem. This was because the British were not only outnumbers but these preachers could be seen as an attempt to destroy local traditions which often led to rebellions and incidents like the Indian Mutiny where it formed a part of the antagonistic attitude that the Indians did not appreciate the least. Thus you tend to see a less emphasis on preaching at least in India. You still tended to see some members of volunteer organizations come and try to convert but they were quickly pulled out if they were found and more importantly if they were found to have insulted local sensibilities. The rise of the usage of Sati for example is a clear since of something which the East India Company banned, since it is against the Christian ethos, which the local Hindu population revived to combat the restrictions against what was seen to be their religion.
Culture was easier, for the nobility, because it was what made you side with the "winners" over the "losers". By adopting traditions from the colonisers the nobility was seen as working with them and they would be more incremental towards the leeway that could be given. This would often be a trickle down effect where the middle class also wanted to project these sort of airs and adopted what the nobility and British did and hence you have the spread of a similar culture.
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