Does the twisting in a twisted pair reduce attenuation?
No. 

The main effects on the characteristic impedance and the propagation velocity are from the diameter of the individual wires, the separation between the wires, and the dielectric constant of the material between the wires.

The main effects of the attenuation are from the lossiness of the dielectric, the conductivity of the wires, and the diameter of the wires.

The main limiter of the bandwidth is from the attenuation, which increases as the frequency of the signal increases (mainly due to the skin effect)