Given the studio already has flashes, I'd suggest buying a set of cheap radio triggers off fleabay to fire them. Or failing that, get a PC lead and trigger them with that. I'd not mess about with an on-camera flash to fire them
As others have said, you need to try and get the subject further from the background if possible to lose the shadow.
You've also got too much light falling on the background in most of the shots. Getting further from the background will help with that - or move the lights in closer and turn them down.
As others have suggested, try shooting raw. That will give you more control with the WB issues. That said, setting the WB to tungsten should have got somewhere close if you were just using the modelling lamps.
Finally, were the images underexposed and have you boosted the exposure in post processing? If you have, that will increase the grain that shows up.