While more answers are always welcome (especially since you include some follow-up questions), for the 45 trillion claim, this thread discusses the claim in detail, and this comment by /u/IconicJester is of particular note. A quote:

But anyone even passingly familiar with trade from the period knows that bills on London banks were effectively the global currency, and the fact that they converted them into rupees in India is just common sense. That the British government paid its bills in India in rupees is not very shocking, nor that they collected their taxes in rupees. What we need to know are the net values for all these taxes and transfers, but that would be a very difficult piece of accounting that would not generate sensational numbers.

You effectively asked 3 questions in your post:

-Was 45 Trillion looted from India?

-Did Indians go from being the richest people in the world to the poorest?

-Was "India" united? If so, why did sepoys fight for the EIC?

The first question is essentially an economic argument, and a tricky and controversial one at that. Unfortunately, this is also the one part of your post that I cannot really answer at all, as I have no significant experience with the economic history of the Raj. I will say that the video linked to in the comment is essentially a summary of Shashi Tharoor's "Ingloriouus Empire." Tharoor's work has been criticized by historians such as Tirthanker Roy for being extremely biased and using antiquated data. You may look into Roy's criticism of Tharoor, as well as John Keay's and Charles Allen's. Hopefully someone more familiar with the topic can comment on this as well.

On to the second question: Did Indians go from rich to poor?

This argument is partly true, India did, prior to the 19th century, represent a very large portion of the world's GDP, however, this did not necessarily translate to wealth for all of the area's inhabitants. Note that from now onwards, for the sake of clarity, when I refer to "India," I intend to mean "South Asia," as some of the sources and data presented deal with modern Pakistan and Bangladesh, both of which were part of large South Asian empires throughout history.

India was, from at least the time of the Muarya Empire, very involved in international trade, and extremely wealthy as a region. Strabo noted that about 120 ships sailed to India annually from the Red Sea, and Pliny wrote that India regularly attracted "at least 50 million secterces." Of South Indian trade, the Sangam poet Kannanar wrote "Here are brought...rich imports (which lie) in thickly pilleed jumbles along spacious streets." Indeed, Indian trade generated an immense amount of wealth well into the Mughal era, however, this wealth did not always directly translate to individual prosperity.

While Indian society was relatively fluid during the Maurya period, the social upheavals experienced during the Post-Gupta period beginning in the 6th century led to a significant hardening of social structure. The majority of the Indian population during this period (and onwards) was composed of Vaisas and Sudras, the two lower tiers of caste society. According to Manu, "a Sudra, though emanicapted by his master, is not released from servitude," as "servitude is innate to him." Sudras were usually not given a specific caste duty, but, instead instructed to do whatever they were told to do by higher castes. Manu specifically notes that "no collection of wealth must be made by a Sudra, for it distresses Bhramins. The Mahabarta states "A Sudra should never amass wealth, lest, by his wealth, he makes the members of the superior class obediant to him." Indeed, most Sudras did not directly benefit from India's vast wealth (although there were occasionally Sudra dynasties, and wealthy Sudras, though rare, did exist). It was, in fact, considered deeply unclean for a Sudra to touch a Brahmin or a Kyshatria, and the defiled upper caste member had to symbolically clean himself with a bath when this occurred.

Underneath even Sudras lay a similarly large section of Classical Indian society, the untouchables (composing nearly 25% of the modern Indian population, according to the 2001 census). Untouchables were not considered members of the caste society at all, and were divided into a myriad of geographically based jatis and sub-jatis (as were other castes, but the sheer size of the untouchable population made this very pronounced). Apastamba Dharmasutra ordains that any studies of the Vedas should be completely stopped for an entire day if an untouchable entered a village. Fei Hsin (a Chinese traveller noted for his accounts of India) claimed that, in Southern India, an untouchable, upon seeing a higher caste member "must crouch down and hide himself by the wayside, where he must wait until he is passed by." Ma Huan, another Chinese traveler, noted that untouchables must "at once prostrate themselves on the ground" upon seeing a higher caste member.

Guilds and other organizations existed among Sudras and Untouchables. Indeed, there existed entire villages populated only by woodworkers, or blacksmiths, or other artisans (as such work was organized strictly along caste and family ties), however, as we have seen, common folk did not profit significantly from the overall Indian production and trade of goods.

Centuries later, in the Mughal Empire, the Dutch merchant Francisco Pelsaert would comment "The land would give a plentiful or even an extraordinary output, if the peasants were not so cruelly and pitilessly opressed." Thomas Roe, a British diplomat, noted that Indian "swyne lye better than any man." While Roe's account was of course massively exaggerated, the common folk of India were not particularly wealth even now. During his invasions, the Emperor Babur noted that "peasants and people of low standing go about naked," wearing only a langoti (effectively a loincloth, still commonly worn in rural areas today). Manucci noted that Indian houses were "constructed of earth and pieces of wood bound together with ropes, without much regard to appearances," with floors "of pounded earth." Of course, not everyone lived like this, (according to Mughal accounts) the Brahmins of Varanasi dressed in fine silks, and there is a Tamil folk story detailing a courtier wearing silks so fine they were nearly transparent. Nonetheless, the majority of the Indian population was not extraordinarily well off, although the levels of abject poverty varied considerably from period to period and from place to place, increasing significantly during times of famine (there are indeed accounts from Manuncci of poor families selling their children into slavery during times of famine, although such accounts were obviously limited to times of significant financial stress).

I will deal with the third and final question in a following comment in a few hours.

While there are great yawning gaps in our understanding of historical incomes, there is no evidence at all that India was ever one of the richest regions of the world. Our income estimates from the "Mughal peak," while higher than the low point of the mid-colonial period, don't even come close to the levels suggested for Song dynasty China, for Italy during the renaissance, or for the Dutch during the golden age. India was poor before colonisation (as was pretty much everywhere in the world) and it certainly wasn't the richest in relative terms. In 1700, on the eve of widespread colonisation, a ballpark estimate based on current historical GDP estimates would be that India had about half the income level of the European colonisers.

The more specific claim on which this misunderstanding is probably piggybacking is that India used to have a much larger share of the world economy, and specifically of manufacturing exports. But here modern analogies lead us very far astray indeed. Long-distance trade in manufactured goods was a vanishingly small part of economies before the modern period. India's large share of this trade, divided by its large population, does not suggest that India was notably rich.

I wonder if I may add to the already wonderful answers you've received from u/IconicJester, u/GaslightEveryone and u/Thecasualgamer15

Wrt your first question, my old answer might be of use to you:

https://old.reddit.com/r/AskHistorians/comments/cl842u/in_precolonial_india_where_european_explorers/faz3xxn

Now the third question. I must say in my view the idea expressed is incorrect. India wasn't united in any way as we might call it. To quote:

https://journals.sagepub.com/doi/abs/10.1177/096834450000700102

But then, it would be anachronistic to condemn eighteenth century Indians, who served the British, as collaborators, when the notion of 'democratic' nationalism or of an Indian 'nation'did not then exist.

Indians who fought for them, differed from the Europeans in having a primary attachment to a non belligerent religion, family and local chief, which was stronger than any identity they might have with a more remote prince or 'nation'.

https://journals.sagepub.com/doi/abs/10.1177/002200946900400106

Perhaps the single greatest and most enduring impact of British rule over India is that it created an Indian nation, in the modern political sense. After centuries of rule by different dynasties overparts of the Indian sub-continent, and after about 100 years ofBritish rule, Indians ceased to be merely Bengalis, Maharashtrians,or Tamils, linguistically and culturally.

I hope this helps!