How do I add other apps to Samsung's multi-window/sliding app in Android 4.1.2? I just got the Android 4.1.2 update. 

I know how to disable the multi-window/sliding app section. I know how to add and remove the preassigned apps there, but how can I add other apps (e.g. camera, calculator, standard music player and other apps I have downloaded and installed)?
You can't add just any app to the multi-window list (the one you get by clicking Edit). That list only contains apps that have been written using Samsung's vendor-specific library to support the multi-window feature. (I suspect that the feature also has special-case code to enable the Google apps in the list such as Hangouts, but that's just speculation on my part.)

You can only make an app appear in that list by contacting the developer of the app and asking them to support it. It may be an up-hill struggle to convince them to invest time and make their app larger to support a feature used by a minority of users on one manufacturer's devices.