Hi Roy,
Here are the answers to your queries:
1. You cannot issue a badge directly via email. First step is to create the badge through badgekit and it will be sent to students via email. Each badge has set of information encoded in it which cannot be done on your email. For this you need to install badgekit and its api.
3. No, I don't think so. The badge will be baked by your badgekit and only thing that student need to do is move this badge to backpack. This may require an additional step which I need to check.
Regards,
Devendra