This is a great answer, I've been trying to find out what the hell is going on with this. Just to add one or two things, both the 1 in 4 women and the 2% of cases statistics have been questioned (imo) pretty convincingly.

the 1 in 4 stat was questioned in this article by noted feminist Emily Yoffre

The Sexual Victimization of College Women, a 2000 study commissioned by the U.S. Department of Justice, is the basis for another widely cited statistic, even grimmer than the finding of CSA: that one in four college women will be raped. (An activist organization, One in Four, takes its name from the finding.) The study itself, however, found a completed rape rate among its respondents of 1.7 percent. How does a study that finds less than 2 percent of college women in a given year are raped become a 25 percent likelihood? In addition to the 1.7 percent of victims of completed rape, the survey found that another 1.1 percent experienced attempted rape. As the authors wrote, “[O]ne might conclude that the risk of rape victimization for college women is not high; ‘only’ about 1 in 36 college women (2.8 percent) experience a completed rape or attempted rape in an academic year.”

But the authors go on to make several assumptions that ratchet up the risk. The study was carried out during the spring and asked women to describe any assaults experienced during that academic year. The researchers decided to double the numbers they received from their subjects, in order to extrapolate their findings over an entire calendar year, even as they acknowledged that this was “problematic,” as students rarely attend school for 12 months. That calculation brought the incidence figure to nearly 5 percent. Although college is designed to be a four-year experience, the authors note that it takes students “an average” of five years, so they then multiplied their newly-arrived-at 5 percent of student victims by five years, and thus they conclude: “The percentage of completed or attempted rape victimization among women in higher educational institutions might climb to between one-fifth and one-quarter.”

In a footnote, the authors acknowledge that asserting that one-quarter of college students “might” be raped is not based on actual evidence: “These projections are suggestive. To assess accurately the victimization risk for women throughout a college career, longitudinal research following a cohort of female students across time is needed.” The one-fifth to one-quarter assertion would mean that young American college women are raped at a rate similar to women in Congo, where rape has been used as a weapon of war.

She also says in a follow up that

It turns out many of the studies rest on narrow samples or wildly extrapolated numbers. (Even New York Sen. Kirsten Gillibrand, a co-sponsor of proposed legislation on campus sexual assault who appears briefly in the film, quietly took the “1 in 5” statistic off her website in December.)

Also I don't know where "Only about 2% of all rape and related sex charges are determined to be false" comes from but I think it might be David Lisak who is one of two people who've done big reviews of false accusation cases. Just because it's easy to find Scott Alexander looks into this here

The rate of false rape accusations is notoriously difficult to study, since researchers have no failsafe way of figuring out whether a given accusation is true or not. The leading scholar in the area, David Lisak, explains that the generally accepted methodology is to count a rape accusation as false “if there is a clear and credible admission [of falsehood] from the complainant, or strong evidential grounds”, and goes on to explain what these grounds might be:

For example, if key elements of a victim’s account were internally inconsistent and directly contradicted by multiple witnesses and if the victim then altered those key elements of his or her account, investigators might conclude that the report was false

Attempts to use this methodology return varying results. Lisak lists seven studies he considers credible, which find false accusation rates of 2.1%, 2.5%, 3.0%, 5.9%, 6.8%, 8.3%, 10.3%, 10.9%. The two with 10%+ mysteriously go missing and thus we get the commonly quoted number of “two to eight percent”, which is repeated by sources as diverse as Alas, A Blog, Slate, and Wikipedia (Straight Statistics keeps the original 2% – 10% number)