How to send author an email after they post content?
One easy way to do that is with the Rules module


Event: After saving new content 
Action: Send email.


Here's an example Rules export (for article) that can be imported via the UI at admin/config/workflow/rules/reaction/import

{ "rules_review_notification" : {
    "LABEL" : "Send review notification email",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "rules" ],
    "ON" : { "node_insert--article" : { "bundle" : "article" } },
    "DO" : [
      { "mail" : {
          "to" : [ "node:author:mail" ],
          "subject" : "[Notification] Content submitted for review",
          "message" : "Your content has been submitted and will be published after review."
        }
      }
    ]
  }
}