1. the shutter speed does not really matter (read your manual for your camera's max flash sync speed and use anything below that)
2. you need to take a reading of the studio flash and not the ambient light
yes, as Judge Ortega said, depends on the colour temperature of the strobes
anyway, the flash tube aging will also affect the color temp, using softbox or umbrella will also alter the color temp, old softbox will also have different color temp, different type or materials of the softbox will also affect the color temp. so custom balance is the way to go.