How are industrialism and self-discovery (i.e., science and religion) during the Victorian era revealed in Heart of Darkness?

The Victorian era in Britain was a time of tremendous advancements in science and sociology, when every year brought new inventions and discoveries. Mastery over both the external environment and the inner workings of the human body and soul seemed increasingly attainable, and the rapid expansion of the British Empire was opening huge swathes of the globe to curious Europeans, enabling a new age of exploration. The key theme in all of this was "progress."
The Industrial Revolution may be at least partially credited with creating the ravenous social appetite for "progress." The ability to create more, better, faster, and cheaper than ever before transformed the economy. It also destroyed and remade the social fabric of the time, as people abandoned their subsistence farms in the countryside in favour of working in the factories. The living conditions for the influx of city-dwellers were abominable, which spurred the birth of welfare initiatives, and the new field of social work. Religious outreach was a common way to care for the working poor, and grew hand-in-hand with social work to make and demand political change on behalf of the disenfranchised.
People felt empowered not just to understand, but to master their world. Things previously deemed insurmountable—like distance—or intractable—like human nature—were suddenly seen as adaptable. Engineering, both scientific and social, could overcome anything, and in the context of Christianity, even the worst of people could be improved and turned into amiable, productive members of society. The Victorians felt it was their moral duty to share this knowledge with the world, especially the "darkest" corners of it, where civilization was pre-industrial and the inhabitants weren't Christian.
This is the context in which Heart of Darkness lies. These are the ideals that Kurtz espouses, with which he opens his report to the International Society for the Suppression of Savage Customs:

"By the simple exercise of our will we can exert a power for good practically unbounded[.]"

The Victorians took an unusually scientific approach to every field of endeavor, recording every hypothesis, experiment and outcome, even in difficult-to-quantify realms such as sociology and psychology. They were keen to maximize efficiency in all things, from increasing crop yields to making effective communities. You can see this scientific approach at work when Marlow describes the Company doctor early in the story:

"The old doctor. . . with a certain eagerness asked me whether I would let him measure my head. Rather surprised, I said Yes, when he produced a thing like calipers and got the dimensions back and front and every way, taking notes carefully. 'I always ask leave, in the interests of science, to measure the crania of those going out there,' he said. 'And when they come back, too?' I asked. 'Oh, I never see them,' he remarked; 'and, moreover, the changes take place inside, you know . . . It would be . . . interesting for science to watch the mental changes of individuals, on the spot . . . '"

Marlow later remarks at a point of serious irritation in his journey that "I felt I was becoming scientifically interesting," as his efforts to remain calm and amiable are failing in consequence of the challenges he's facing. He can feel the "mental changes" the doctor mentioned beginning to take place inside him.
These same "mental changes" are what twist Kurtz's original desire to "exert a power for good practically unbounded" into a desire to "Exterminate all the brutes!" The influence of the landscape in Heart of Darkness is one that corrupts fresh-faced Victorian ideals and makes them unworkable. The heat and humidity, the tropical diseases, the intractable jungle, the lack of any "civilizing" factor like a police force or an established religion, all combine to ennervate the Europeans and make them weak and vicious. Their high-minded desire to improve the lives of the natives while making a tidy profit for themselves is revealed as a foolish daydream. It is not possible to do both, for the profit can only be made on the backs of the natives, and enslaving them is the antithesis of "improving" their lives.
Heart of Darkness inverts the Victorian love of progress and shows the cost at which it is often attained. In the Congo, the ugliest face of industrialism appears, without any counter-balance from religious or social outreach programs to ameliorate the lives of the workers. The Congolese are not merely enslaved, they are quite literally worked to death in the service of maximizing the Company's profits. The Europeans' journey of self-discovery is one of discovering the profound cruelty of which they are capable, and how indifferent they can be to that cruelty, so long as their pockets are lined. Back in Europe, a polite veil is drawn over the Company's dealings, and much emphasis is placed on the "civilizing" influence of the European outposts in "darkest Africa." Most people Marlow encounters back home are ignorant of the Company's true nature, and even, like Kurtz's Intended, convinced that it is achieving wonderful things. The desire to see progress everywhere leads to a collective delusion about the way that progress occurs—as long as the "Wheel of Progress" keeps turning, no one is much interested in knowing about the people crushed underneath it.