The short answer is no, you aren't going do any damage with a wireless charger being near any magnetically sensitive devices.
Let's tackle each one of the points you brought up.
Inductive charging is only effective up to a maximum of 4cm (about an inch and a half). Anything past that and the magnetic field is simply too weak.
It would need to be "right on top of it" to be close enough, but that point is moot. See #5 below.
Time is irrelevant when it's out of range. Again, it would have to be on top, but it's a moot point.
Same as #3
When your wireless charger is not attached to the Apple Watch, it's not transmitting an the electromagnetic field used for charging. Within the base station is a "communications and control" unit that regulates how much power to use to create the magnetic field. When a device is not in range, it will output very nominal power. Once a device comes within range the "comm and control" unit will negotiate how much power to output to charge the device.
Granted, this is a very simplistic description of the charging process, but the key concept is there.
Bottom line is that when not connected, the magnetic field is so low that you would have have remove all of your drive's enclosure, electrical shielding, and casing of the drive itself to actually affect the magnetized platters. With the watch charging, you would have to somehow keep the base station watch and drive in direct contact with each other which is next to impossible due to physical constraints.
If you notice, your watch must be in direct contact with the charging station for it to charge. You can be assured that the electromagnetic field being generated is going to be very weak past the physical dimensions of the watch.
More info: Qi Wireless Charging
Backstory...I came upon this info while researching how to build my own Qi wireless charger under a glass desk. I have a frosted white glass desk which if I put the transmitter coils in a particular area, you wouldn't be able to see that a charger was in fact part of the desk. All you would have to do is place your phone on the desk in the right spot and it would start charging. Unfortunately, I couldn't make it work because the glass desk, being 5mm was too thick to use Qi (same used in the Apple Watch). I would need a resonant charger to get the distance, but it was incompatible with my phone.