it’s called a ferrite core, which is basically a special magnet around the cable to eliminate any noise (interference) that may come from other cables or devices
it will not power it, just charge and transfer files. When you plug it in the Garmin goes into transfer mode and will not show routes an guidance etc
Well... that depends on what model Garmin it is! If it's a car nav then it will run off the USB mini lead. If it's a bike one then it'll be cradle or self-powered.
you could also run a lead direct from the battery, I don’t recommend using the external power points as things fall out of them in the move etc, even got melted by the exhaust.