I've only just bought my HDR2000T so I'm not familiar with all the options.
I want to be able to copy some (SD) programs to a usb key drive, do I need to eject the drive when copying is finished, if so, how?
I don't normally bother - once the light stops flashing and/or "copying" status is no longer present in the on-screen menus it's finished. Never had any problems. The reason for ejecting a drive in Windows is in case the data is buffered for background transfer.
If you really do want to eject the drive, there are options on the hidden menu. I don't know how to access it on an HDR-2000T, but for HDR-FOX see Things Every... (click) section 9.