1: The claim that people who report rape are more likely to be doubted by authorities and the general public seems to be true.
Depends on which "authorities". Police, prosecutors and courts operate in a system that still has pesky things such as presumption of innocence, burden of proof set at "beyond a reasonable doubt" and due process protections such as ability to confront one's accuser. These authorities then have to be selective in which cases they bring forward based on available evidence - and even then they sometimes get it wrong and go after innocent men like Brian Banks.
College authorities on the other hand don't have to do that since the horrible Obama administration directive that set burden of proof at the lowest level of "preponderance of evidence" and basically eviscerated any due process protections of the accused. The result is that the woman is believed automatically and in practice the man has to prove his innocence. This leads to cases like University of North Dakota where a man was expelled even though the police actually charged the accuser with filing a false report and University(sic) of Georgia and Vasser where there were no criminal charges brought because there was no "probable cause" evidence yet the man was expelled in each case. That is not justice, that is prejudging based on gender. That is eviscerating rights of one group of people to ostensibly protect another based on their genders.
2: I have yet to see any solid evidence that that particular offense has been proven to have a higher incidence of false reporting than any other crime.
Only if you take Susan Brownmiller's fake number as revealed Truth.
3: There have been many cases of police departments ignoring or not following up on rapes, even going so far as to not complete the testing of their handy 'rape kits.'
The huge backlog of untested "rape kits" is indeed a horrible injustice and one argument I agree with radfems with. On the other hand, that does not excuse punishing other men when there is no evidence that they did anything wrong. Especially consensual drunken sex where the man is presumed to be a rapist and the woman is presumed to be a victim even though they were both drunk and engaged in sex consensually. Btw, these are the cases where "rape kits" are all but useless as the sex is not in dispute. Which is the reason why rape is a crime most difficult to prove - it involves an act that is usually perfectly consensual and legal.
4: Assaults, sexual or otherwise, on women by men based on their appearance or dress seem to be much common than on men by men, or any other combination, for that matter.
However men are much more likely to be victims of violent crimes than women are. Yet female victims are given much more consideration than males are.
5: Assaults on women seem to be more frequently blamed on the victim than assaults on men are.
The problem is that with sex there often is no evidence that would distinguish nonconsensual sex from consensual sex and consensual sex is something millions of people engage in every day. With mugging, battery, murder the cases are more clear cut and victims of those are by and large men.
These observations lead me to believe that there is something wrong with mass perception of this. Whether that can be called 'culture' is semantics, and is largely irrelevant, compared to the reality of the situation.
Well true "rape culture" would be a subset of "violent crime culture" but if you look at all violent crimes you can't play cheap 70s-80s style gender warfare politics (Brownmiller, Dworkin, Steinem, McKinnon et al). Also many radfems consider innocuous things like porn as part of "rape culture" as well.