How can I customize the page titles, taglines, background, and other settings for the different post types and single posts?

You first need to enable the page settings for the post types you want to modify.

Go to Appearance > Theme Settings and scroll down to the Content Settings Section.

Here you can enable settings for each post type. You can enable Global settings (that will effect every instance of that post type) and you can set Single post settings to customize for each post. You can also enable both if you want to set global settings and then just override one or 2 things individually.

Once the global settings are activated you can set them in the Content Settings tab of your theme settings. Be sure to then select the correct post type (right under the tabs).

Once the Single post settings are enabled you'll see an Apex Page Settings metabox within each post that you can use to override global settings.