I am not able to use a FireWire device in my Virtual Machine.
Parallels Desktop (9-11) supports only storage devices (Thunderbolt and FireWire), i.e. external hard drives - are supported.
Parallels Desktop (9-11) for Mac does not provide support for non-storage FireWire devices, i.e. scanners, printers, video/sound cards, etc. - are not supported.
If a monitor is connected to Mac via Thunderbolt and it works fine with it, there will be no issues with the virtual machine either, in case this monitor is not connected to the virtual machine directly as an external device.
Thunderbolt and FireWire devices are not supported by Parallels Desktop 8 and earlier.