1) I'm gonna have to agree with this one, when ever she shows any sort of negative action, a lot of the fandom seems to blow it out of proportion(I mean look at the comments at EQD when the released the extended synopsis for Sleepless in Ponyville and how everyone was flipped their shit on Rainbow just for telling freaking campfire stories before the damn episode even aired, and after it aired, some still complained)
2) But she is a tomboy, but there's absolutely no negative connotation with the word, all it means that she has a more boyish nature than most girls do. Just to clarify, Applejack is also a tomboy, it's just not as obvious as Rainbow Dash
3) This feels more the result of annoying stereotyping than anything(whether it actually is is up for debate), though the fact that most of the characters are female helps. Also she does have her fair share of straight ships which has been gaining steam, but in all honesty the lesbian shipping isn't a big deal, and doesn't really factor if the people hate her or not. To be fair if people hate her, she either wouldn't be shipped at all or be shipped with Cupcakes Pinkie
4) I've seen this a lot top, though I've never figured out why
5) If Rainbow Dash really was one of the most hated characters in the show, Cupcakes would be a lot more popular. But alas, neither are hated for involving Dash, Cupcakes is hated because it's a demented take on a fairly innocent show that serves no purpose than to make the reader sick to their stomach, and many fans hate it for how it portrays both Pinkie Pie and what happens to Rainbow Dash throughout the story. For MLD, many probably hate it because they find it overrated(As a Rainbow Dash fan myself, I could honestly care less about that fic)
In my opinion, yes and no. She does get some of the most hate in the fandom, especially after season 2, but she's also has one of the biggest fanbases as well so I guess that sort of negates everything. I think the biggest reason why RD hate is very noticable is because her hater tend to be an incredibly loud bunch(and to be honest, based on personal experience, I think they tend to be some of the biggest assholes in the fandom, with them presenting their opinions in a douchey and rude manner, behaving like bigger jerks than the character they say they hate so much)
Granted not all of them act like that, I've meet some friendly ones, and some have good reasons for not liking her(not everyone has to), it's just that I come across a lot more that act like that
tl;dr
She's not very hated, people just have loud "opinions"