Yes, they control hashtags. It is a censorship issue. They lie about what's trending, every, single, day.
There's a global problem with Twitter censorship, to the point it has a Wikipedia page: https://en.wikipedia.org/wiki/Censorship_of_Twitter
2) The Wikipedia page primarily concerns cases where Twitter is ordered to engage in censorship by other countries, not Twitter choosing to censor opinions on its own . I wish they would tell Ergodan where to stick it, but that's not the same as them posing a threat to your speech or mine (assuming you're not from Turkey).
Let me ask you an unambiguous question. I am a citizen of the United States of America, a country with a strong tradition of freedom of speech. Can you offer me any reason to fear that I am going to be censored by Twitter for expressing an opinion (liberal, conservative, fascist, even)? To be perfectly clear, and avoid confusing matters with the issue of harassment, say that I do not @-mention other users.
https://twitter.com/BrittPettibone/status/797186228894322688
On the other hand, I can't quite replicate her search. When I search, I get more results than she does, maybe not as many as I'd expect, but importantly, not the same as her. I can't say "obviously there's nothing here" but I also don't think there's a smoking gun.
If you're concerned about this, you really should not be pointing me to one tweet by one user. You should have reams of evidence, documented, with a timeline, with comparisons to what other users see, etc, etc. If you don't care about convincing people who haven't already bought in, that's ok, but if you do want to persuade, you're going to have to provide something better than this one tweet. (Case in point, downthread, we have a person who's convinced they were shadowbanned, then all of a sudden they check, and they aren't: https://news.ycombinator.com/item?id=12935624).