With regard to prices and the relative value of money then and now, it really depends on what measurement metric you're using. This site, which I've recommended on r/AskHistorians before, will help you with conversions for specific sums: https://www.measuringworth.com/

The thing to remember is that different commodities had different proportional values - so food and clothes, for example, ate up a much higher proportion of people's incomes than they do today, while rent was substantially cheaper.

Working class wages in the middle of the nineteenth century were in the region of 20 to 40 shillings per week, depending on the level of skill involved. Servants earned less, skilled engineers more, for example. Women and children were paid less than men. Less than 20s. a week was insufficient for a family to live on. (Remember, there are twelve pence in a shilling, and 20 shillings in a pound).

In terms of prices and the cost of daily living, a few figures which might help. A one-pound loaf of bread cost about a penny. However, many poorer people lived in rented rooms without kitchen facilities, and so would buy their food ready-made. You could eat at an 'ordinary', which was a kind of tavern or restaurant serving a fixed menu at a fixed price. The three-penny ordinary was most common, for which you would usually get meat, bread and beer. A sixpenny ordinary would be more elaborate, and might include pudding.

As regards rent in London, the absolute cheapest option was the 'doss house'. For about fourpence a night, you could rent a single bed in a communal dormitory. Some of these doss-houses were reasonably clean and respectable, others were squalid. The better kind were single-sex, usually occupied by working men, sailors between voyages and so on; but the worst were often mixed-sex and crime-ridden. If you wanted to rent an unfurnished room or a couple of rooms, you would pay in the region of 1 to 3 shillings a week. The poor lived in much denser accommodation than the middle classes or the wealthy - it wasn't unusual for a room or two to hold a family of 6. Area-wise, Soho was neither especially rich nor especially poor; it was an area popular with immigrants, and there were a lot of craft workshops there, making everything from silverware to carriages. The absolute poorest parts of mid-19th-century London were St Giles's (the area to the east of modern-day Tottenham Court Road station, since demolished to make way for New Oxford Street), the 'Old Nichol' in Bethnal Green, Whitechapel, and Bermondsey (south of the river). These were true slums, or 'rookeries' as they were known at the time, once-grand houses divided up into cheap rented rooms, with no proper sanitation.

I'll run through your other questions fairly briefly. Teenage and child employment was very common, and labour laws were quite lax - they were indeed paid less than adults. School attendance wasn't compulsory until 1880, although prior to that, children might attend a charitable 'ragged school' until the age of 10 or 12, for basic education. Teenage and child prostitution was also common. The age of sexual consent was 13 until the 1880s, when the reformer and journalist W.T. Stead conducted an exposé of child prostitution, 'purchasing' a young girl to prove how easily it could be done. In terms of the price paid for commercial sex, it could be as low as a shilling or two, and as high as a pound, depending on the good health, youth, attraction and location of the woman involved.

What counted as a rare luxury? Well, given the cost of clothing, when everything was cut and sewn by hand, a new and well-made suit, dress or pair of leather shoes would definitely count as luxurious - the poor tended to buy their clothing second-hand. A man's new suit could cost between £2 and £6, which could be a month's wages. Imported and perishable foodstuffs, such as exotic fruit, would be expensive due to their rarity. Jewellery, of course, was expensive, so a ring or cravat-pin with gemstones in it would be seen as quite flashy. Watches varied... it was possible to purchase a relatively cheap, basic watch in a brass case, although the finest examples with engraved and enamelled gold cases would cost tens of pounds.

I can't say how much it would have cost to study medicine in London in this period. But yes, absolutely, doctors of this period had more-or-less a full knowledge of human anatomy; of the skeleton and circulation system etc. Dissection had been used in European medical study since the Renaissance. Also, by 1850, germ theory was in its infancy, but was beginning to impact on medical hygiene.

One primary source you can peruse is Mrs. Beeton's book of household management. Though she is mostly writing for a higher economic and social level than your characters seem to be, she has approximate prices for her recipes that are time specific, and also goes into lease laws for better to do families at the end of the book. You'd also get a sense of what kind of food was seen as good at the time. Don't take is a holy writ, because this was idealization for sure, but is will give you numbers for actual things.