What is going on? Did the heat in the external enclosure damage the drive?
It is impossible to say for sure, as we can't for sure say if the heat is a symptom or a cause. I would tend however to support your thesis, though, as heat affects magnetic properties of materials.
Although it is unlikely that your HD reached any close to the curie temperature, heat can still weaken the magnetic proprieties of materials, as cold improves them. It might be (but this is just an hypothesis) that the magnetic proprieties of the disk surface or of the writing heads have weakened.
Also, heat can have deformed the physical shape of some component, making them less effective (for example a writing head which is now further away from the disk surface).
A test you could do is to wrap your HD in a watertight plastic bag and immerse it in a bowl of crumbled ice (even better: you can mix the crumbled ice with salt, that brings the temperature down to circa -21°C) and repeat the tests there. You might notice an increase of performance.
Incidentally his is a technique that - through contraction of the materials - is also useful to unstuck movable parts (which does not seem your problem, as normally a stuck movable part means no read and no write capabilities at all).
Another common cause of disk failure is vibration. Vibration brings lack of precision in the moving parts, tear of joints, wrong alignments between heads and disk surface, and so on and so forth. In case something is now impeding the disk to revolve smoothly, you would for sure have extra heat generated by both the friction and the increased power used by the engine to keep up the rotation at the same speed. In this scenario heat would be a symptom rather than the cause of your problems.
Why can I still use the drive without any problems other than a slow write speed?
With a metaphor: for the same reasons for which you will go faster on a well lubricated bicycle than on a rusty one. Modern hard drives are smart enough to compensate for hardware problems, so - unless a core component is broken - they will find a way to keep running (this is so because HD's obsolete very quickly, and if they would stop working at the first writing error or corrupted sector, you would be changing your HD every few weeks).
What is going on with this SMART Status and what does that Quick Test result mean?
Unless you find some official documentation, this is a question one might only infer the answer to. You can pick your favorite one: from marketing reasons (so you do not immediately notice defects!) to human mistakes (it's just a bug, it should report "not passed") transiting by design ones ("pass" means the HD is still usable, the test that fails signal the fact a non-essential subsistem is broken)
Should I expect this drive to die on me any second?
Again: you can never know for sure. I have still a 5 Gb unit from the 90's up and running, for example. But consider this: you normally would keep backups of a totally healthy HD because it might - all of a sudden - fail. Now, you have an HD with visible signs of bad health status, heating up like crazy, having degraded performance and failing tests... if I were you, I would definitively hope for the best but prepare for the worst!
Hope this helps, and if you try the cryo trick (the ice thing) I would be very interested to know the outcome of it. Best luck!
USB2 running in "hi-speed" can theoretically do about 60MBps (MegaBYTES) maximum (AKA 480Mbps), but you'll never get that.
If you are using both drives on the same USB hub (as it appears in the picture), then you are sharing that available bandwidth between the devices. So at theoretical best (with both drives being accessed) you'd probably only get like 30MBps to each drive. After adding overhead and real-world physics to the mix, then getting ~15MBps (BYTES) sustained sounds about right to me.
You're not going be able to reassign which USB ports are attached to which hub, without some very good soldering (at least). :)
You're going to want to get that 2nd drive onto a different USB hub, or hooked up via Firewire, eSATA, or alike to get it onto a different data bus.
Best Answer
If you put an external harddrive next to the server/desktop and:
then I see no reason why they should not last just as long as internal drives.
Ofc, there is a reason why people buy external drives. And they often do get exposed to one or more of the conditions I mentioned above.