Question 3a : When is it safe to disconnect the Tux Droid from my computer?

You can always disconnect the dongle or switch off Tux. It shouldn't pose any problems for the TuxBox software.

Question 3b: Is this even when tux box is opened on your pc?

Only when you have the web radio gadget running this might cause problems on the PC. But besides that, there is even a way to troubleshoot: Unplug and plug your dongle again while the software keeps running.