1,她這樣多次在電話裏留言謾罵我,我應該報警還是應該請律師呢?
You need a police report. If she stated who she was during the phone call, you need reflect that in the report. Then ask for a TPO (Temporary Protection Order). If she violate the order, then police can arrest her.
Harassment calls are not police's favor case. Even they found the phone number, it is real hard to prove that she actually made the call. Especially from cell phone.
2,她如果再次開車跟蹤我的汽車,我是否應該立刻報警?警察會管嗎?
Yes! Start make notes on when and where she followed you. Also every single harassment calls as well.
3,有的朋友建議我應該提前去警察局備案,可行性強嗎?
Yes you need do that. Some people can get real bad down the road. Police report will help you.
4,如果還有其他人在中間挑撥或謠傳,那算不算屬觸犯法律呢?
You dont know that. You should not guess.
I will change number. I will look for another job. It is not worth to fight. Take defensive position and walk away.