Is the whitelisting of allowed file types user configurable and are we able to see what is on the whitelist?

Yes we can configure the allowable file upload whitelist for each account (although we recommend against this in order to simplify security management)

Our whitelist can be specified as a a Mime type or File extension. 

This is an advanced account configuration, that Brandkit Support  must action for you. 

We do not allow customers to manage whitelists, but you can supply your own list of MimeTypes or file extensions to whitelist or request a change, and we will action.

The current default whitelist can be seen here: http://help.brandkit.io/getting-started-with-brandkit/requirements-and-specifications

Happy branding  :)