Q. Can I create a Subject Readings list for myself or to share that isn't for a teaching site?

Yes. You can create a reading list for yourself that isn't associated to any Moodle site. However, please note that if you publish this list, others can still view it via the 'FIND LISTS' feature. To maintain privacy, you can keep the list unpublished. 

You can also create a list that's associated to a project (PROJ) or training (TRNG) Moodle site, it doesn't have to be a subject Moodle site.