The first thing to note here is that ITV's/PBS's Sanditon does not show Jane Austen's depiction of the Regency period - it's Andrew Davies's, the showrunner. Austen lived from 1775 to 1817, and she wrote the partial manuscript of Sanditon at the end of her life, well into the Regency period; while I guess we could look into how realistic it would have been considered at the time, I think what you're wondering about has to do with the deviations Davies and his team made to the text. The original MS goes up to chapter 11 or 13, basically just introducing most of the characters. (Austen's chapters tend to be fairly short by our standards.) Almost everything that happens in the show is an invention of the modern writers: Miss Lambe never appears on the page, and Dr. Fuchs, the Stringers, Otis, Eliza, Mr. Howard, et cetera are completely made up to add to the cast. There is a juvenile novel by Austen called Lady Susan, recently adapted into a movie called Love & Friendship, but the main character of that story shares nothing but a name with Sanditon's Lady Susan.

Moving on from my pedantry ... this kind of question is extraordinarily hard to answer, as the scope of accuracy is all encompassing, ranging from nitpicking the shape of a sleeve to much broader issues of "would a person in that situation have done that". I'm going to hit at a few things, and if you have questions about any specific ones, feel free to ask about them.

Women's hairstyles. Let's get this baby out of the way first. The women's hairstyles are incredibly inaccurate. At their best, they tend to be modern updoes with clearly defined curls around the head or involved in the bun; at their worst, they are not hairstyles at all, just hair that's been allowed to be loose. A few women have plainer updoes with a single long curl hanging over one shoulder, which is essentially an 1870s style that likely developed in the Victorian era in order to look 1770s, and it is wildly out of place in the Regency. Women simply did not leave their hair loose during the day during the 1810s - even female children typically wore theirs up, once they were old enough to start growing it out, as the idea of putting one's hair up being a sign of adulthood dates to the middle of the century. There were two options for hairstyles: the hair could be pulled back into a coil and pinned in place (what we now call a bun), or it could be twisted into a chignon and held with a comb. Often, the very frontmost edge of the hair around the face would be cut short, to curl naturally or to be curled with papers/rags or curling irons. There is literally one hairstyle in the entire show that is decently accurate to the period - Charlotte's hair at Lady Susan's ball in London.

Georgiana Lambe. Were there biracial women in Regency England? Yes! In the original text, Miss Lambe is actually said to be "half-mulatto", with the obvious implication of slavery one or two generations back in her family background. William Makepeace Thackeray included a similar character a few decades later in Vanity Fair, partially set during the Regency, another heiress from the West Indies who is introduced as a school friend of the heroines and then later as a potential bride for a social climber. White English men went as colonizers to both the West and East Indies in order to get rich - in the case of the West Indies, they usually attempted to purchase many enslaved people, and then force them to grow and process cotton or sugar. Many enslaved women were raped, and many biracial children were born - many of the latter were simply considered the property of the plantation, but some were accepted by their white fathers and considered of a higher social status. There was also plaçage, a widespread system of unofficial "marriages" between white colonists and black or mixed women that was often quite appealing to the women involved and, with "husbands" of higher levels of society, allowed them to live very leisured lives. It is far from implausible that a young woman of color with an inherited fortune could exist during this period.

I'm happy to respond to any specific things you're wondering about. Much of the show is problematic as a period piece due to issues that are not quite on an inaccurate/accurate axis, so it's difficult to nail down what I should discuss here on my own - for instance, the way Sidney and Charlotte talk to each other cannot be said to be "inaccurate", as a wide range of behavior took place historically, but it would have been considered extremely rude and far too intimate. And I could note that an heiress's abduction could be foiled, but the fact that it had occurred would likely cause her to be ostracized from society if she did not marry her abductor, since the possibility that she had been raped would always be considered.