Questions on PCGU1000 signal generator

I have got some questions on the PCGU1000 signal generator:
Does this signal generator stop working when I switch off the PC to which I connect it for making the settings or does it run further on the last setting?
Can it be modulated with an external signal? If yes, what kinds of modulations are possible?

Yes, it continues running if the USB cable is disconnected.

No.

Can a short-circuit on the signal exit destroy the device or is it short-circuit resistant?

No damage - it is short-circuit resistant.