black widows. who are they? here's a few bits of lore taken from various comic runs:
the program is called black widow because it refers to spider AND its purpose to train girls into becoming ruthless spies, but generally the trainees are given other names ( both as identities and code names if you will ) not necessarily spider themed
the mcu turned nat's backstory into an hive mind sort of situation but what you need to know is that actually:
the trainees go under a biochemical engineering process where their immune system is boosted, it prevents aging and provides fast healing. along with this they're chemically subjugated with a pheromone based serum ( to keep them loyal ) and an anti pregnancy type of serum that immediately kills cells - the doctor who designed this explains that the program wanted killers not mothers, hence something so aggressive. all these effects can be reduced by taking specific med suppressants as showed by natasha during her investigation on stefanya's case
natalia was brainwashed into believing to be a ballerina from the bolshoi as part of her kgb sleeper agent training. there's no indication the red room would brainwash other trainees into having these memories though they were given a training regime similar to those of ballerinas
there isn't a specific age to enter the bw program. natasha was 10 during her first cycle, enrolled by her legal guardian. another instance is yelena enrolling voluntarily at 15, with her parents fully knowing about it
the red room had a parallel organisation called department X. that's where the winter soldier program started ( for those who don't want to go with mcu's lore that it was hydra ) though called project zephyr. there were at least three more winter soldiers other than bucky, though as far as we know he was the only one eventually sent to the red room as a teacher
whoever switched to department X / sleeper agent program, was also given another serum. effects of that would be super strength, even faster healing etc
natalia escaped the red room several times and for long periods of time, every punishment done on her was eventually blueprint for how the next batch of widows would be treated in the program - some of the trainees who know natalia have some grudge against her because of this
the graduation ceremony is essentially a proof of loyalty. natalia's was the hysterectomy and the forced marriage to alexei. yelena's was investigating on a crime apparently committed by her mentor and the circumstances of his death - bottom line is that generally trainees are put through a traumatic event where someone they should not care about is involved, and to pass the loyalty test they basically have to do whatever it's asked of them. whoever fails to follow orders dies, obviously
natalia has had the highest score for decades. it took years for yelena to finally surpass her, but the point is that after her defection the red room was actively looking for someone skilled enough to replace nat as THE black widow. they never had much luck about that
as of today, unless a writer shows up and changes the lore, all red room have been destroyed by nat and bucky along with some secret hydra bases.
everything about zephyr project was destroyed in 2012, the three winter soldiers are not operational anymore
in 2016 anya / brown recluse along with her mother ( the original headmistress ) started a new version of red room called dark room - still based in the ruins of the original red room. natasha destroyed it
in 2017 after waking up post death, natasha finds out that there's a secret red room cell in the usa where almost every widow has clones of them made in series, ready to replace them whenever the previous body dies. in order to destroy the cell from the inside, natasha becomes headmistress of the red room for three months, actively training new recruits although by the end of it the girls are returned to their families with the help of SHIELD
yelena never outright says it but did mention a certain interest about wanting to train lucy ( and other girls ) red room style. she mentions a different, less competitive approach but natasha is categorically against the idea and won't let it happen in their san francisco operational base
