If you are using PowerTeacher Pro, teachers can create a "Conduct" assignment worth 100 points, give everyone a 100, then deduct points as needed throughout the Trimester.
If you have Conduct as a separate class the grade will have no bearing on the grade of the original class. I also cannot speak to State/Provincial Reporting Requirements (if any) of where you live. You could make "Conduct" a Category and make as many assignments as you like. If you use Category Weighting as your grade calculation for Trimesters you could weight it however you'd like. It wouldn't be a separate line on the report card but individual grades are viewable on the Portal.
Create a new Course, create sections and enroll the kiddos. You may want to put it in a period that exists outside the Bell Schedule so you don't have to worry about attendance. Again, I cannot speak to any reporting requirements.
No, there cannot be a score in the negatives. I cannot imagine a scenario in which you would need to have one, honestly; a zero is a zero.
PT Pro does not have that functionality. You would have to change the 100 to a 95. You could use the comment on the assignment to track +/- entries.