Would anyone know how i would go about opening the app draw from within my
application or know how to show a list of each application installed on the device
and allow the user to run them?

yes, there should be some way to list the applications installed on the device because all apk's of the applications reside in the /data/data/app directory.
so u can list the applications using that list of apk's.[font=Arial] [/font]