Running a program as root on Android
Ugh, that's 4 questions in one. Our site works best with one question per post; but let me try:


How to install via CWM (custom recovery)?
usually, it's "install update.zip from SDCard" when the deal is to "install something via recovery". By default, there should be an update.zip file in the root of the SDCard, which you then navigate to and select.
Hint: I always update it via Google Play (the "normal way"). Works smoothly, never had trouble, doesn't require a reboot.
Is the choice "Install SuperSU into /system" supposed to still be possible to select after a successful install?
I'd say "No", but it depends. This usually moves the app from /data (user-space) to /system (system-space). After having moved it, it should no longer be in its original location. But depending on how updates are installed (SuperSU e.g. updates via Google Play, like any other app), this update could again end up in user-space, in which case the user might wish to "repeat" the system integration.
How do I run an arbitrary program as root?
Two-fold. First, "arbitrary programs" (apps) must request root access themselves, you cannot make them "run as root". That's a little different when it comes to the command line: prefixing your commands with su makes the terminal app requesting root access. So you could e.g. list all directories below /data using su ls /data and succeed (while a simple ls /data wouldn't be able to access all files/sub-directories here).
Is it normal for SuperSU to "close" itself spontaneously while looking through the settings?
I've never experienced that, and I'm using SuperSU on one of my devices for a year now (the others have chainfire's SuperUser). But I must admit I'm not often calling it directly and stay there for longer. I mostly only see the access requests of apps, or the update recommendation via Play :)