Whenever I teach anthropology I enjoy the old adage that the goal is to make the bizarre mundane and the mundane bizarre. To that end, when I teach about genital cutting I always like to discuss its history in the US. Most people are quite aware of male circumcision especially since there are movements now to end it. But the vast majority of my students are unaware that cliterodectomies were once performed legally in the West as part of a medical procedure. To that end I've read a few peer reviewed pieces I've found on JSTOR about Isaac Baker Brown, psychology of the ovary, and his procedure (which easily compares in brutality to the narratives students read about FGC in Africa.)
Students are usually fascinated, horrified, and full of questions not all of which I have the answers to so I'm hoping you can help fill in some gaps. How common were cliterodectomies in the mid 19th century as medical solutions to things like epilepsy, depression, nervousness, "vice", etc.? Any estimates on how many women were subject to the procedure? How did the general public feel about it - was it accepted or seen a bit of a quack procedure? How did the women feel about it afterwards? Were they angry, satisfied, depressed, or what? What about their husbands? During his trial Brown said the procedure had been performed since Hippocrates - how accurate is that statement? And since the operation still continued to pop up time to time in medical texts how much did Brown's fall from grace really impact their frequency?
I do not know much about the history of female cutting in Europe. I haven't seen any references from primary sources promoting it in the 21st century. And even in the 20th century, it appears to have been regarded as an American medical peculiarity (e.g., 1893 French summary of US female circumcision promotion itself summarized in the Cincinnati Lancet-Clinic). As Brown's professional censure demonstrates, European doctors appear to have been much more opposed to cutting for girls in contrast to the numerous genital surgery enthusiasts in the US, a significant number of whom were equally enthusiastic about female genital cutting as they were about male.
Clitoridectomy was never promoted routinely, not even by Brown. It was only presented as a potential cure for more serious conditions like epilepsy, insanity, and masturbation that was resistant to cure by less aggressive surgery (e.g., Terry, 1900). It was even directly opposed by some proponents of female circumcision. Still, it's odd how obviously barbaric it was, yet it was never addressed by the US medical community for being unethical.
Here is a woman talking about her "medical" clitoridectomy that would appear to have occurred in the 1960s: Medicalized female genital mutilation 13 min.
While that extreme surgery existed. It was never popular and was never applied routinely. If you were not aware, the primary form of medicalized female genital cutting was genital skin and membrane cutting, the same as for the male. In US medical history, female genital skin cutting was promoted by many of the same doctors who promoted male genital skin cutting. Genital surgery enthusiasts said that among other problems, antisocial behavior could be caused by clitoral abnormalities that were best treated with excisive genital skin surgery. There are more than a dozen references about it in /r/intactivists/wiki:timeline of medicalized genital cutting including: Kellogg 1888, Morris 1893, Fisher 1895, Brown 1897, McFarland 1898, Lewis 1899, Freeman 1914, Dawson 1915, Eskridge 1918, Rinehart 1921, McDonald 1958, Rathmann 1959, Wollman 1973, and Crist 1977. Or a more accessible source is this article from earlier this year that's just about the female cutting tradition: Female Circumcision as Sexual Therapy: The Past and Future of Plastic Surgery?
For instance, in 1921 "orificialist" Jacob S. Rinehart, a Missouri physician wrote of circumcision:
Ninety-nine per cent. of the babies, both boys and girls, require circumcision at birth.
Some of the moral effects (as well as the physical) of the circumcision of the boy has long been recognized. But few, today, including physicians, recognize the fact that girls are equally benefited by circumcision, and, furthermore, that any of the forms of irritation (already mentioned) of the sexual system or even of the rectum may be the source of sexual self-consciousness. This frequently leads to masturbation in both girls and boys. Such children need pity; they are usually nervous and irritable, and possibly willful. These conditions are responsible for the immorality of our schools, for the prostitution in society, for gonorrhea and syphilis, and for many of the unworthy marriages and divorces. Hence, while we are solving the problem of chronic diseases we are also solving the problems of society. It has been agreed, by all physicians with years of experience in this line of work, that every prostitute has some form of sexual irritation producing sexual self-consciousness. The proof of this phase of the orificial philosophy, as with the chronic physical and mental diseases, lies in its manifold cases of practical application, the many who have thus been restored from a life of shame and disgrace to one of purity and hope.
Here are a few more direct links to historical sources about it selected from that timeline.
I have no idea about any of your other questions, but as to how long the procedure has existed, it was included at least in the seventh-century Paul of Aegina's On Surgery (6.20). I'm not as familiar with the Hippocratic corpus, but since Paul talks about it it may indeed have been included there as well.