Are there legs or a stand with this item or does it lay flat?

The WD My Passport drive rests flat on the desktop on very small rubber "feet." These feet are small (2 mm) half-spheres that elevate the drive a couple of millimeters from the desktop surface.

what is this used for ?

I used this to temporarily store data while upgrading computers. I went from PC to MAC OS X so it was quite a feat for me. It stored what I needed then, and now I use it to transfer from on realm to the other. It has been very reliable! No issues or flaws what so ever.

What's the reason for the custom USB on the drive end? (pointing at WD).

It's a WD proprietary connector. Why they opted for this is open to question and has been the subject of some less than complimentary comments. The main complaint is that the cord length is pretty short and makes using this drive with a desktop inconvenient unless you purchase a USB 3.0 extension cable.