first of all, thank you for choosing Origami, and my apologies for the delay in my reply!
I can see that the link you’ve provided above uses another theme at the moment, yet I will go over the questions just in case, in the same order:
1). Origami currently does not support second-level submenus, yet we will add this to our list of features for the next theme update. Thank you for the idea!
2). In case you mean the “Appearance -> Customize” admin page, please make sure that you’ve upgraded to the latest version of WordPress (4.3) and are using the latest version of the theme (1.2), which you can always download from the “Downloads” tab of your ThemeForest account. If you are already using both of the above and the page still does not function, please let me know, I will continue the investigation.