Do we have evidence of two neutron stars orbiting each other, particularly in this galaxy? If so, what is the signature like (period)?
As for what would happen to the Earth from a nearby SN/GRB - that depends on the 'nearby'. Also keep in mind that the pulse width is short - e.g. ~100 s or less - based on a quick check of a few articles. The GRB would affect only the side of the earth facing the GRB.
Relationship between the Gamma-Ray Burst Pulse Width and Energy Due to the Doppler Effect of Fireballs
Y.-P. Qin, Y.-M. Dong, R.-J. Lu, B.-B. Zhang, and L.-W. Jia
Gamma-Ray Burst Light Curves Another Clue on the Inner Engine
E. Nakar and T. Piran
Gamma-Ray Burst Peak Duration as a Function of Energy
Gamma-Ray Burst Physics with GLAST