Let me try to summarize a little bit:
1) Witness calls local radio to say that she heard no explosions, that she heard shots only from one gun, that she saw a black SUV from the police hitting tamerlan and that the cops shot him afterwards.
- at the same topic there is evidence about bombs exploding at Laurel st, as well as witnesses to a shootout between the police and tamerlan, meaning that he also shot them. So two of the four claims she made are wrong. I'm sure she is not lying, but maybe her point of view was not that good? A black SUV did hit tamerlan, but was it the police one or the stolen one? As a witness she would be quickly dismissed by a jury. :-/
2) The first medical examiner says that he did not see any tire marks or the usual stuff you see when someone is run over by a car.
- at the same topic we see the gruesome photo of tamerlan's wounds as if he was indeed hit by something big, the death certificate stating the same thing and at least two witnesses, including the lady at the radio show, saying they saw tamerlan being hit by a SUV.
3) A photo taken by someone that lives in Laurel st showing the moment seconds before tamerlan was hit by the SUV. Here you say that the path dzhokar took is unreal while others say it's possible.
- as this photo is the only presented evidence about the path, there's no way of proving anything in any direction.
4) Dzhokar was unarmed and surrounded, inside a boat, and police shoot him unnecessarily.
- I agree with you. Although they were pissed of, maybe a little afraid of guns and bombs and probably tired with the whole neighborhood combing (how could they miss that boat?) , they probably should have done it differently. If they indeed killed him with those shots, the overall "there's something fishy here" would be much much worse. As was said by someone here, it's very easy to say that when you are only spectating, but as a tax payer, that's what I would like them to do - be a little less jumpy.
5) You didn't comment on that, but another point is if the police should have fired 200-300 rounds during the persecution, risking injuring people inside their houses, while trying to capture the suspects. I strongly think they shouldn't, and I think people should be discussing that, as it is a real issue. Again, instead of debating a possible need of better training or excesses from the officer, there's a lot of energy being used to discuss hoaxes, false-flags, crisis actors and so on ...
So, addressing one of your questions, I do think police is a little more violent than expected, and that it could improve a lot.