Can I (legally) use one licence key for Parallels on my desktop and laptop or do I have to buy a second licence? Are the licences per machine or per user?
License keys are per activated program. You need separate license key for each installation of Parallels Desktop/Workstation you have. So you can either buy a second license key for the laptop installation or uninstall the program from the desktop and install it on the laptop using the same license key.