Is the Pope allowed to notarize various Vatican documents?
As the Head of State of Holy See (Vatican), the pope can notarize various documents within the Vatican, especially Papal Documents written by the reigning pontiff. In such cases, the pope would use the Ring Of the Fisherman to confirm an official document written by himself.
Originally, the Fisherman’s Ring was a signet which was used to seal official documents signed by the pope. The private correspondences of the pope were sealed by the use of the Fisherman’s Ring while the public documents were sealed by stamping a different papal seal onto the lead that was attached to the respective document. During the 15th century, the use of the Fisherman’s Ring changed and it started to be used for sealing official documents referred to as papal briefs. This practice ended in 1842, when the lead sealing was replaced with wax. - The Pope's Ring
The pope's signet ring is one of two papal seals used in documents. The other one is a leaden bull (bulla).
The earliest mention of the Fisherman's Ring worn by the popes is in a letter of Clement IV written in 1265 to his nephew, Peter Grossi. The writer states that popes were then accustomed to seal their private letters with "the seal of the Fisherman", whereas public documents, he adds, were distinguished by the leaden "bulls" attached. From the fifteenth century, however, the Fisherman's ring has been used to seal the class of papal official documents known as Briefs. The Fisherman's Ring is placed, by the cardinal camerlengo on the finger of a newly elected pope. It is made of gold, with a representation of St. Peter in a boat, fishing, and the name of the reigning pope around it. - The Catholic Encyclopedia
Pope Benedict's signet ring will be destroyed using special silver papal hammer to ensure documents it was used to sign will not be forged.