Is there a permission in Mediawiki that allows a user with username A-User to create and edit pages A-User, A-User/A-new-page etc but not to edit other pages?
Not by default. You can find the list of permissions here, and the permissions each user group on a wiki has at Special:ListGroupRights. There is
editmyuserjs which allows users to edit user subpages ending in
.js, but probably even that requires the normal
It would be pretty simple to write an extension granting that right, though. See UserPageEditProtection for a similar example (which does the opposite: instead of granting the right to edit own subpages, it takes away the right to edit others' subpages). You could make it do what you want by tweaking the return values in the userCan hook a bit.