MacOS – Why won’t Special Characters display certain characters

That looks like the front-end processor window for some non-Roman scripts. This gets pretty far into the weeds if you don't normally use them, but in case you're curious:

With a writing system like Japanese, you type using English characters to produce phonetic Japanese characters, and then convert those into ideograms. For the most part, this happens "inline", that is, right where the cursor is, wherever you'd be typing if you were typing in English. Back in the old days, however, it happened in a separate window (the FEP window), and once you had a chunk of text composed in that, you'd send it to the main window.

I use Japanese on my system. The FEP window still exists, and every once in a while it will pop up for a second—then the system seems to get its composure back and I go back to inline typing. I'm guessing that you're trying to produce a character that involves multiple keystrokes, like ü, and somehow that's invoking the FEP window. I can't say why it's happening or how to stop it, but in my experience it is harmless.

You can resize the window, but it's different than most windows in Lion.

If you click and drag a corner or an edge, the window will resize. Yes, it doesn't look like you can use the corners, but they do work.
This appears to work with every corner except the top left, which is blocked by the close button. Edit: Actually, if you aim just right (to the top left of the close button) you can use that corner too.

To summarize: Things still work, but the active areas are tiny. You just have to be careful.

This behavior is strange, and seems buggy to me. I expect than a future update will fix this and allow you to resize by all the corners and edges.