Ah I see. So the large silver enclosure and the computer chip looking thing on the opposite end are different from the diode? What exactly are the proper names of those two components, seen in the picture below?
from the pictures you posted i clearly see that your diode's window is burned,this can be happend if any kind of junk burns in the window.there are two options to fix that,you buy a new bare diode or you can sent your laser to someone that can decan the diode for you.(after that you need to extra careful with it to not get any junk on the diode)
That's what I thought too, but the image wasn't quite clear enough to say for sure.
So when I was using the laser to burn things, I could put the tip as close as possible to the object I wanted to burn (sometimes I would press it against it) to maximize its strength, steady the laser, and block the bright reflection. Is that a bad idea?
That's a bad idea, you want some distance there. Otherwise you end up with gunk on your optics which ends up destroying the optics completely.