In order to verify the signature, I would like to be able to see any information they used in creating the signature (such as ssn, date of birth, etc.) and see whether changes have been made to a document. What I don't want to have happen is just have to rely on the third party for authentication and have them just tell me "it was signed." I want to be able to access the full audit trail. If this is the case, does that mean I have to pay for / create the account with the third party that I then allow the signer to create an account through?
You can look at Signature Properties, which will show the full chain to the trusted root. You can't see the signers details that they used to get the certificate issued, because those are not in the certificate nor are they anywhere else in the chain. (Thats why you have a Trusted root certificate -- the Certificate Authority takes responsibility for the identity of the signer)