Yes & yes, but you don't need to use it or install it. When you plug the drive into your PC it automatically shows as another drive letter and you can then use it in the same way you would your C drive etc. Enjoy.
I think that's more of a software question patrick (depends what your using to view your movies). However, if I'm watching a download straight from the hard drive I can certainly play and pause it. If I shut it down or remove it though it won't remember where I was
Assuming you are using it with a PC obviously you will need it to be connected in order to install the program and tell Windows that you wish to install it on that drive. Windows registry will note where it has been installed and consequently will expect to look for it on that drive. Obviously, providing the USB drive is connected the software will work OK. Broadly all external drives that have been added and formatted by the PC will treat the drive the same as any internal drive. I note Geoff has stated the same reasoning, however for a USB3 drive to be quick the PC has to have a USB3 port to connect to. Also the port should be on the motherboard, ie generally a socket at the rear, as front ports are generally fed by an internal cable. For this big drive it may not feed enough power even if the port is designated as USB3. Still your question wasn't about access speed was it.
My laptop is only usb 2.... and I have no problem, a usb 3 has a split pin cable, it will still take a usb2 cable to charge it though....
I think of it as dual possibilities rather than problems. Hope this helps.