Power loss shouldn't do any physical damage to the disk since most of these use the inertia of the platters to safely park the head when they lose power, but if you were writing the the HDD, damage to the file system might still be possible but very unlikely in newer drives.
As for these connectors, enclosures, they have nothing special, just use safely remove to eject the drive and let it rest a few moments just to spin down.
These converters have nothing special, just a circuit board that converts the signal coming from the SATA controller to the USB. Most external drives are like that, if you open any external HDD, you'll find a slim normal (mostly 5400rpm HDD) drive with a SATA output connected to a circuit that converts its signal to be connected to a USB.