Is there a way to assign this permission level? Currently the lowest permission level that allows adding is Contribute. Unfortunately this allows users with this level to add/edit/delete all posts in this list? How can I make it so users can add to the list, but only have the ability to edit or delete their own posts?
If this is a List and not a library then this functionality is built-in. Simply go to List Settings - Advanced - Item level Permissions and you can configure exactly this behavior