Safari playing a youtube video in the background

Can you open the Console application (in the /Applications/Utilities/ folder) and see if anything is reported up to and during the application hangs?

Are you actually getting a crash or just a hang? (A crash will display an "unexpectedly quit" dialog on its own (creating a .crash file) , whereas a hang will require you to explicitly force the application that's not responding to quit, which will then generate a .hang (" stopped working because of a problem).

If you are actually getting a crash, please post the crash log (as much as you can) or otherwise provide access to it (as they can be somewhat long). If it's a hang, perhaps any output to Console might be more informative than the .hang report.

You mention iTunes does not start at all: do you mean it immediately starts to hang when you try to launch it, or does it crash with an unexpectedly quit dialog?

Also, try launching Activity Monitor (also in /Applications/Utilities/) and be sure to set the "Show" popup menu to All Processes. Check once at launch or on a fresh startup to see if there are any processes highlighted in red. Then when you begin having the problems, check again in Activity Monitor to see if there are any processes shown as not responding; if so, please post the name of them along with any info that's reported to Console.

My rough guess of what's happening is that either coreaudiod itself, or another sound/multi-media-related framework or launch-on-demand agent or service that these apps need is not responding, which in turn causes any applications that rely on it to hang as well.

Forcing Safari to quit works reliably for me. Double click the home button,tap the 'X' on Safari.