Liz,
If you already have a Facebook App created, I'd recommend using that app with JFBConnect. You shouldn't need to create a new application to use with JFBConnect, just add the existing Facebook App ID and Secret key into JFBConnect and have our Autotune software update your application with the right settings to make the app work with Facebook Login and the other features we enabled.
In general, you should only have one application per website. If you need to create a new app, you can switch the names and do other stuff like that, but it just shouldn't be necessary.
For the redirection from your Facebook Page, that's probably because you don't have an SSL certficate on your site. See our
SSL Certificates for Facebook
guide on how to get one. Once you have one, you can use the Page Tab integration features of JFBConnect to show your website inside of your Facebook Page.
Hope that helps explain, but if not, let us know,
Alex