It's not accurate.

To deal with the revealing dress issue first:

Whether or not women sometimes revealed their nipples in public is still under discussion among fashion historians. There are several French fashion prints from the eighteenth century that show women with their nipples on display, but they're problematic to interpret: for instance, Little Mother at a Meeting in the Champs Elysées and Young middle class woman dressed in a Polonaise , both from the Galerie des Modes in 1778. The first example here is sexually-charged even without the exposure - this is a young woman, alone, meeting someone for a "rendez-vous" in a grove off of a fashionable avenue - and the Galerie has a habit of leaning on eroticism in poses and descriptions. ("The pose of this governess prevents her fine leg from being seen; her breast is lily-white and covered by a ruffled handkerchief, but it can be found by Lubin," is my favorite example of completely unnecessary sexy description.) As all of the people upvoting this question can attest, images of and talk of breasts produces results! Other examples of commercial prints that show women with exposed nipples seem to combine satire and sex appeal, such as A Peep into Brest with a Navel Review, a bawdy joke about the British naval campaign against France in the Atlantic, in which the Lord Admiral patrolled near Brest to keep an eye on the French, or are just an excuse for voyeurism, such as L'Essai du Corset, which doubles the voyeurism by letting the viewer look at the men looking at the woman in the print.

What the costume designer may have been drawing on was costumes from the seventeenth century. Sketches made by Inigo Jones for masques at the English courts of James I and then Charles I in the 1600s-1630s exist - you can see two of them here at the British Library, and an Elizabethan costuming website hosts a greater number, taken from two books on Jones's work. (I've also found a blog with even more images, but there's no indication of the source for the images.) The costumes for female masquers frequently feature a tight-fitting bodice with a U-shaped cutout under each breast, much like the gown used in Outlander, though there is often a little light veiling used for support. These designs may have been used to emphasize the physical femininity of the performers in these private theatricals, in comparison to the men who were allowed to play women on the public stage. Either way, there's no evidence that the tradition continued to the later seventeenth century, let alone the mid-eighteenth - and we don't even know how closely these sketches were followed at the time, as no costumes survive. A miniature of Queen Henrietta Maria in a costume by Jones from 1632 certainly shows no such license - her neckline is very respectable, and filled in with a partlet - though a miniature of a lady playing "Flora" does show the extremely low "neckline".

As far as nipple piercings go - there is no good evidence for them before the twentieth century. There is a lot of writing out there in pop histories of tattooing and piercing that asserts things we have no sources for, or that we have very tenuous evidence for. To quote from a previous answer of mine,

Queen Isabella of Bavaria popularized "garments of the grand neckline" that were open down to the belly-button and led to women rouging and piercing their nipples

First, her name is more commonly given as "Isabeau", so that is a good clue that the many representations of the story are coming from a single, unscholarly/uninformed source. Isabeau was married to Charles VI of France, and was frequently a part of courtly diplomacy and the mediation of disputes between powerful aristocrats; when her husband began to decline into mental illness, she took on more responsibility and acted as regent. Eventually civil war broke out, and in the disorder Henry V was able to swoop in and win the famous Battle of Agincourt.

If you're at all familiar with the history of women actively involved in royal politics, it's probably not that surprising to learn that after she died, commentators enthusiastically condemned her and created a reputation of decadence, lust, debauchery, and incompetence out of whole cloth. I haven't been able to track the story about piercings to a specific primary source, but if it exists it's almost certainly part of this tradition. (Isabeau is a pretty interesting figure and if you'd like to learn more about her, I suggest Tracy Adams's The Life and Afterlife of Isabeau of Bavaria.)

There was a fad for "bosom rings" in the late 1890s in Paris and London.

The only evidence that this fad ever existed appears to be certain letters printed in English periodicals (Society, The Family Doctor and People's Medical Advisor, English Mechanic and the World of Science) in 1899. They were intermixed with correspondence about savage boarding schools, whippings, tight-lacing, and high heels that Dr. Valerie Steele considers to be examples of fetish fiction rather than real exposés, and most likely do not represent real practices. Essentially, r/thathappened material (or Penthouse letters) of the 19th century.

The designer for Outlander is certainly accomplished, but this is the first production in her profile on IMDB that is set before the twentieth century. There are a number of inaccurate costumes in the show, largely based on unfamiliarity with the period and an interpretation of artwork without a full understanding of the context around it, as well as the fact that costume designers aren't fashion historians and don't have the same goals or needs.

A couple of sources:

Women on the Renaissance Stage: Anna of Denmark and Female Masquing in the Stuart Court (1590-1619), Clare McManus (Manchester University Press, 2002)

Fashion and Popular Print in Early Modern England: Depicting Dress in Black-Letter Ballads, Clare Backhouse (Bloomsbury Publishing, 2017)

I should give credit to Isis Wardrobe for putting me on to several of these visual sources. For those who actually click the link: yes, that blog post is arguing the opposite of what I'm arguing. I simply disagree with the conclusions because I think the context of the artwork (as something to be marketed or make a point) undercuts is value as proof of everyday behavior.