1. If someone gives you a negative trust, can you fight back like proving yourself correct and removing the negative trust from your profile.
To put it simply, you can. Keep in mind though that a negative trust given to you by someone can only be removed by that same person.
2. what advantage you get if you give someone a negative trust?
I can't say you get "advantage" from it. It's a feedback system that shows others what they might be dealing with. It's like giving a 2 star rating to a restaurant you dislike. It serves as a warning.