vineyshafts The issue with apps and icons shifting around is often caused by launching the game in fullscreen mode but at a different resolution than your monitor. (Sims 4 does have a 2560x1440 mode but doesn't use it by default even on ultra settings and with a monitor running at that resolution.) The desktop should go back to normal when you quit the game, but when it crashes rather than closing the normal way, that may not happen.
The easy workaround is to launch in windowed mode, at least until Sims 4 is running properly. Open Options.ini, in Documents > Electronic Arts > The Sims 4, search for fullscreen , and set it to 0 (zero).
For the crashing itself, is Sims 4 installed to your external drive? Sometimes the game doesn't get along with drives formatted as exFAT, or slow drives in general. If it is, try installing it internally instead. Even if you don't want the game on your internal drive in general, this is a useful test, especially since there's nothing obviously wrong in your dxdiag, and there are no Sims 4 errors listed.
If that doesn't help or isn't relevant, let the game crash again, then look for new errors in the Reliability Monitor. Click Windows key-R and enter "perfmon /rel" without quotes, and you'll see a chart of errors and updates with a column for each day. Today is on the right.
Look for an error that happened at exactly the time of your most recent Sims 4 crash. If you find one, double-click it to see more details, then copy that info and paste it into a reply here. If you don't see a new error, check back in an hour or so—the Reliability Monitor doesn't always update right away.