About the TQ warning you should be more specific, by reporting the actual failing paths.
Anyway, from the screenshot saying 'unconstrained paths' I guess your tutorial doesn't fully constraint the design, probably I/O ports.
This is a common (and bad) practice in tutorials and sample designs which avoid the full contraints for sake of simplicity and (I think) for better portability of the same design on several eval boards. However the involved frequency in such cases are quite low and usually these warnings don't affect your system operation.
The message box in the second screenshot means you are using TSE core in OpenCore mode, i.e. in demo mode without a permanent licence: the core will stop working if you close that message box or detach the USB Blaster cable. Then simply DON'T press the Disconnect button and probably you will be able to successfully go on with the tutorial.