Footer .PNG Editing

This depends on how the footer image is used. It may be controlled by the theme or plugin. Can you post a link to your site?

You can change the image but unless you name it the same exact thing, it needs to be changed in the code. Since your theme is a child of twenty twelve, most likely it will only be able to be reached using ftp. I highly doubt you will be able to edit it in your control panel but it’s hard to tell since you have a custom child theme.