In both cases, I have to ask the same question. How long are you waiting on that black screen with the spinning circle cursor? There is always a tremendously long delay before the Launcher/game becomes responsive again after I get a successful sims3pack install, always has been and it seems to have gotten longer over time (and as I've added more content over the years). If I just wait it out, eventually things resolve and become responsive again. Not talking hours here, but many many minutes perhaps.
The black screen on quitting usually happens to me whether or not I've saved but when during the current game session I have not moved the game clock forward. Perhaps I was in session just to build, create/edit sims in CAS, or to look something up, but not really to "play" at that time. Others have reported it more often than that, but the game still manages to quit gracefully after "a while." When in windowed mode, I can always work with other applications (surf the web, etc.) while waiting for either condition to clear up.
Am on Win 7 myself, by the way. And in case the tremendous delay after quitting (not so much after installing something) is due to web data being slow to update, perhaps try playing offline - that is, logged off at the Launcher and in-game levels and keep the TS3 store online shopping experience switched off within Game Options if you don't already do these things.
Compatibility Mode should not be required regardless, and for most players it tends to cause more issues than it solves.