Doug
You might want to check out this http://openbadges.learningassistant.com/ from Mozilla on Open Badges. It will explain most of the background to answer your questions.
Badges are not something created by or for Moodle, but an implementation in Moodle of Open Badges, which is an open source project made by Mozilla, already in use by lots of software in many industries besides education.
To address your specific items:
1) Badges are downloadable since the whole idea is they belong to the person issued to, the recipient. The recipient can download them to save to a badges collection known as the "backpack" - which is theirs and has nothing in particular to do with Moodle at all.
2) This is on purpose: badge templates deleted at the system or course level are archived, not truly deleted.
This follows the Open Badges principle that once awarded, a badge belongs to the recipient, not the issuer. So badge once issued exist on its own, regardless of the status of the original badge template it came from. (My old junior high school exists no more, but I still have my diploma.)
An issued badge has a unique URL that goes back to your Moodle site to allow validation. It needs to find information such as issuer, criteria, and other evidence of its validity somewhere. While the original template badge may not be active anymore, that data is required for reference ("evidence").
Currently, badges issued in error (for whatever reason) don't yet have a method of "revocation." Mozilla is very aware and working on how to do that.
3) You don't have to make the images, as Mary noted, but you do have to make each badge. That is, you have to create each badge in Moodle with its criteria and so forth. A badge is the image file + the metadata associated with its recipient, issuer, criteria, a unique identifier, and so forth, and this metadata is 'baked' into it when it is awarded and issue to a user.
Basically, once awarded, a badge is on its own out in the world, property of its recipient. Revocation will arrive one day, but as always ...
Award wisely ;)