hi nicdain,
Did you ever try remove the sharing folder of your USB30 disk and add it back?
I have a Lacie USB30 disk with exFAT filesystem, and no your issue.
for your 2nd question,please try below steps:
1. connect your device to host Mac OS first.
2. go to Settings->USB&Bluetooth pane of you windows 7 vm from Fusion.
3. I suppose your Toshiba disk is listed in the USB&Bluetooth pane.
4. Then you need to check it on and see what will happen.
As far as I know the usb3.0 device is not supported perfectly in Fusion Windows 7 OS.
The root reason is the usb3.0 driver for win7 VM is not good or not work at all.
I am not sure if the Toshiba Disk can be recognized normally in your Windows 7 OS,
but there should be some prompt pop up as you expected.
so, could you please tell me the results if you can try above things?