Only way to add new fields and process those fields is CB Auto Actions or a custom plugin. onAfterEmailUserForm can be used to add new fields to the form the same way CB AntiSpam does with captcha. onBeforeEmailUser can then be used to process those fields and add that information to the email. Both triggers variables are as follows.

onAfterEmailUserForm
onBeforeEmailUser
Most variables are references so for example you can modify the message of the email and add the fields to it. There is no functionality to add BCC/CC/Attachments from this trigger though if that's what you're needing.

What are those email options supposed to do? It's easy enough to render whatever HTML you want there using onAfterEmailUserForm, but adding some sort of functionality/storage to that HTML is more complicated.

Ok, then you should be able to do that with the above 2 triggers in CB Auto Actions. Both auto actions would be Code actions. For onAfterEmailUserForm you'd just be using an HTML code action and output your checkboxes by setting Mode to Return under the Output tab. For onBeforeEmailUser you need to set Variable 7 as a Reference Variable under Parameters then use a PHP code action to modify that variable using $variables to add your checkbox value to the message being emailed.