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1/ 半个多月过去了，还没收到警察报告，正常吗？我需要催保险公司吗？ 

The police report usually comes out within a week.  You can go to the police department website of the county where the accident occured, and most county has police report on the web searcheable by name.  It might take it longer for insurance company to find it.

Or you can just give the police department a call.  You speak English, yes? 

It could also be the state trooper, instead of the county police.  They might have two different system.  Depend on who actually responded.  

2/我平时是在dealer 处保养，是否需要去让他们验一下车？还是等保险公司的消息后到指定验地方验车？

The designated repair shop of the insurance company who pays the repair. 

3/ 不是我的责任，我用了保险有了历史肯定要涨保费吗？

No, your insurance only goes up if the accident was your fault. 

4/在等待时间我还需要做什么？如何做？我不可能去警察局催，因为路途遥远，反复催保险公司合适吗？目前车况不影响开车行驶。

See #1, go on the web

5/我还在等警察报告，里面有对方的保险公司信息，还知是哪一家公司，需要找律师咨询吗？没有人员受伤。

See #1.