Alight flashes at position x=0m. one microsecond later, a light flashes at position x=1000m. in a second reference frame, moving along the x-axis at speed v, the two flashes are simultaneous. is this second frame moving to the right or to the left relative to the original frame?

To the right relative to the original frame.

Explanation:

In first reference frame S,

Spatial interval of the event,

Temporal interval of the event,

In the second reference frame S', the two flashes are simultaneous, which means that the temporal interval of the event in this frame is

The speed of the frame S' with respect to frame S = v.

According to the Lorentz transformation,

And positive v means the velocity of the second frame S' is along the positive x-axis direction, i.e., to the right direction relative to the original frame S.