Can anyone offer me some help on how to change my username and other settings using the android cellphone application?
It doesn't seem to be possible to edit user profiles from within the Android app. The Meta Stack Exchange page that introduced it does not mention it, and the feature request Ability to update profile from the StackExchange Android App has been open since October 2013.
It's unclear what you mean by 'settings'. On the desktop site, going to your profile > Edit Profile & Settings > Preferences, there are what would normally be considered 'settings' for the site - there's really no chance of those being editable from the Android app.
On the other hand, if you click the menu button (upper left hand on the app) and scroll to the bottom, there is a Settings button that allows you to control the notification settings (on/off, vibrate on/off, notification sound, quiet hours), but that's about it.
And to emphasize a bit - if you have questions about the network-wide functioning of the engine, and particularly with specialized topics like the Android and iOS apps, the mother meta at Meta Stack Exchange is a much better place to ask.