Check the extraction for the receiverID when you defined it in the document type to make sure that your msg has the particular field and it has some valid data.
You have to check in 2 places in the TN DocumentType IdentifyingQueries for ReceiverID(set the xpath that will extract the id from the document select DUNS or Userdefined etc…based on the partner profile you have in place),check ProcessingRule criteria for the sender/receiver/documentType are set properly and note this rule should be above the default rule.
Make sure the above conditions satisfy and get your document successfully recognized in TN.
Yes you can post the same document to any number of partners, all you need to do is simply add the logic to post the document to different partners in the service which is getting called by your processing rule