Hi Brian,
Yes to upgrade, just re-install the module on the site.
Regarding with the css file, it is recommended that you make the changes on your skin.css rather than on module.css itself in the future.
Just consider the upgrade wise, because the module.css will always be overwritten.
So make the changes on skin.css to overwrite the module.css is a good thing to do.
For the template, if it is a custom template that is saved on the database, it will not be overwritten, but if you modify the .ascx file directly, it will be overwritten.
Always do a backup first before upgrading.