Go to Settings and see where it says the default download directory is. Make sure this directory actually exists, and is one you have write access to (not C:\Windows... nor C:\Program Files... or something like that) ... also I've heard of Opera crashing if there are certain foreign characters in the name, so nothing complicated. See if doing that helps.
Ugh. I'm sickened by how dumb the solution I just found is. I tried changing this from the default (C:\Users[username]\Downloads) to another directory, but I saw the same behavior. Then I decided I'd be a smartass about it and use the Windows 10 "Documents and Settings" shortcut. So I changed my default save directory to the following: C:\Documents and Settings[username]\Downloads
It works. Which is both gratifying and really disappointing because that's a stupid thing to work. That's literally pointing to the exact same folder that "C:\Users[username]\Downloads" was. Why does this work? Why is this so dumb? Bleh. Thank you very much for the help. I'm very glad/bummed that it worked out.