Air coolers for the win.

Doesn't look like corrosion, since that would likely be a blue/green color from the copper (you can see a little of that oxidation in the third pic), but it probably is a buildup of minerals as the main plate has slowly leaked fluid out the sides.

Should you use it?

It's leaking fluid. Unless you know for a fact it's using some kind of non-conductive fluid, it's a matter of when it leaks onto something more important, not if—probably your GPU, if not your CPU.