It would be convenient, but I'd think it would also be a serious security liability. They'd have to take great care to only pass them directly to another well-vetted app.
Not easily. Those Safari passwords in OS X are stored in the Keychain application. I have seen work arounds like this that use a script to export the passwords to a text (CSV) file.
Safari is the browser I use 95% of the time. On occasion I'll use Opera and Firefox. In both, under Preferences, there is an option to sync saved passwords from other browsers (hence, probably from the Mac Os Keychain). I have not used it personally, but, I notice that both Opera and Firefox require you to set up a personal account, first, before the password sync will work.
I don't know anything about Google Chrome as I do not use it.