The apps configured to show on the lock screen is completely independent to whether the live tile can update / app show toast notifications. I’m not sure what the limit on the number of apps that have live tiles is but it is much higher than that (and may even be resource limited).
You trying to run the apps will have no effect on toast notifications. Either the app will receive push notifications, which means the OS will launch / pass messages onto the app transparently to you as they are received, or the app will have a background agent that will run itself on a timer, again transparently to you. If they are saying they need to run in the background, then it is the latter and this is not something that requires any input from you beyond perhaps setting some preferences in the app to start with.
Not the best examples of apps that use a common framework as MICROSOFT writes the Facebook and Twitter apps so they are written for winphone from the ground up. They are also completely different to the iOS / Android versions with full use of panoramas, win phone design guidlines, etc. (although the new beta of facebook that MS have just released goes back on that a bit :-( )
Does indicate you are ill-informed and diminishes your argument.