Manage the image gallery in mosaico
The answer is to the first of your two questions is: the images are stored in a subdirectory of the CiviCRM "Image Directory", which by default looks like [civicrm.files]/persist/contribute/.

The specific subdirectory it stores it in is: images/upload

You can see the code on line 153-ish of this file:
https://github.com/veda-consulting/uk.co.vedaconsulting.mosaico/blob/2.x/CRM/Mosaico/Utils.php

The answer to the second of your two questions is: yes. If you create a new traditional mailing, you'll see a button in the wysiwyg window that lets you add/remove images. That tool will manage the same directory that Mosaico uses.

The answer to a question you didn't ask "how can a new mosaico mailing make use of existing images" is: along the top bar in the mosaico interface there's the same button (i.e. a picture of a mountain) which let's you reuse existing images in your "gallery". So you could also manually put a bunch of images into the images/upload directory for your civimailers to re-use.