I have a similar question, so I'll just post it here:
How do I remove the battery status icon in the notification bar? I use an app with numbers instead of the built-in thing which is just a vague color-coded semi-filled blob, and it really just takes up space.
to answer both of your questions, no you cannot remove any of those things from the notification bar. If you were to flash a custom rom then you would be able to remove just about anything from the notification area. droidhive has about 3 or 4 different roms for the Bionic that allow you to do this.