Hi Victoria, I'm glad to help. For badges, it depends on the code in question. Certain types of code, e.g. javascript and iframe, are not allowed on WordPress.com for security reasons. You can find out more information here: https://en.support.wordpress.com/code/
If it is HTML code, then you can enter it into a text widget: https://en.support.wordpress.com/widgets/text-widget/
Let me know if you are still having trouble with badges code. If you have any other questions, please create open a new support request so that it's easier to organize the answers: http://en.support.wordpress.com/contact/
Thanks and good luck with your blog!