PKCS1 v 1.5 Signature questions
PKCS #1v1.5 signatures are basically signed hashes. Therefore, it is possible to extract hash and applied hash algorithm (in ASN.1 DigestInfo format) from properly signed signature.

In some old terminology, this operation may have been referred to as "encryption with private key". However, this terminology should be deprecated as the private key operation does not provide security you would expect from encryption (confidentiality) but instead it allows to ensure that signing has been made with private key matching public key used in verification (authenticity).

See RFC 3447 / PKCS #1 v2.1 for new version of PKCS standard. It calls the underlying signature primitive RSASP1.

Quoting that document:


  The main mathematical operation in each primitive is exponentiation,
  as in the encryption and decryption primitives of Section 5.1. RSASP1
  and RSAVP1 are the same as RSADP and RSAEP except for the names of
  their input and output arguments; they are distinguished as they are
  intended for different purposes.