In Office 2010, I created a Normal template with certain styles. I then created other group templates based on the Normal template. I want to update certain styles in both the Normal template as well as the other templates. How do I do this? I believe also want to change all of my styles to check off "New documents based on this template". What exactly is this option and is there a way to modify all of the styles rather than having to modify each one in each template?

First, as to your last question, you do not want to do this. You do not want the default to be to change the template. I don't know that it is possible, but I do know it is a bad idea.

Once a template is created, its styles are divorced from the normal template. If you want to transfer styles, you would want to copy them using the Organizer. You can record a macro copying styles from a certain template to the current template. This concept is explored more in: A Global StyleSheet in Microsoft Word

Thank you regarding the first question. Regarding my second question, I should have been clearer. If you look at the Modify Style window for any style, there is an option to apply something "Only in this document" or "New documents based on this template". What does this do? There also is the same option in the window that appears under the Edit tab of the Manage Styles window. What does this do? The other option I believe you may have been referring to is the option to "Automatically update", which I agree generally is a very bad idea.

Checking that option transfers the changes made to the template that the document is attached to, generally the template used as the basis for the document.

Normally information flows from a template to its document. Checking that box temporarily reverses that process.
What is the relationship between a Microsoft Word document and its template?

Thank you. The hyperlink to the article you noted was also very helpful.