Sensitivity analysis gives ranges, and a new constraint can only hurt

Consider the statements: 1. Sensitivity analysis provides a single value within which a parameter may change without affecting optimality. 2. While performing sensitivity analysis, the upper bound infinity on the right hand side of a constraint means that the constraint is redundant. 3. When an additional constraint is added in the LP models, the existing optimal solution can further be improved if $z_j-c_j\ge0$. Which of the above are correct?