Yes, by adding a custom field to the taxonomy with the type image. Locations by default include this image field, other taxonomies do not.
Yes. Using the Backend Display Editor, add the field (Listing Description) to the summary display of the listing. See the documentation on customizing displays.
Currently, this is limited.
This is not currently possible.
Currently term data is cached up to 1000 entries which may cause some terms not to appear. One can alter this limit manually in /lib/components/Entity/Helper/TaxonomyTermsHelper.php
Edit line 25:
->fetch(empty($num) ? 1000 : $num);
They plan to add a hook for this to allow configuration from the backend in the future.