May the parties into legal cases decided by the Supreme Court request private repositories like Lawphil and Chan Robles to remove/delete their names?

Article III of the Constitution of the Philippines contains the Bill of Rights. Section 2 states that "the right of the people to be secure in their persons, houses, papers, and effects against unreasonable searches and seizures of whatever nature and for any purpose shall be inviolable, and no search warrant or warrant of arrest shall issue except upon probable cause to be determined personally by the judge after examination under oath or affirmation of the complainant and the witnesses he may produce, and particularly describing the place to be searched and the persons or things to be seized. Section 3(1) states that the "privacy of communication and correspondence shall be inviolable except upon lawful order of the court, or when public safety or order requires otherwise, as prescribed by law."It further states that "any evidence obtained in violation of this or the preceding section shall be inadmissible for any purpose in any proceeding." Section 7 states that "the right of the people to information on matters of public concern shall be recognized. Access to official records, and to documents and papers pertaining to official acts, transactions, or decisions, as well as to government research data used as basis for policy development, shall be afforded the citizen, subject to such limitations as may be provided by law."

It was said the right to privacy is not absolute where there is an overriding compelling state interest.   In the case of Morfe v. Mutuc, the Court, in line with Whalen v. Roe, employed the rational basis relationship test when it held that there was no infringement of the individual’s right to privacy as the requirement to disclosure information is for a valid purpose, i.e., to curtail and minimize the opportunities for official corruption, maintain a standard of honesty in public service, and promote morality in public administration.

Article 8 of our Civil Code also provides that Judicial Decisions applying or interpreting the laws or the Constitution shall form part of the legal system of the Philippines. Logically, the decisions covered under this law inludes all factual elements.

On the above premises, the parties on legal cases decided by the Supreme Court cannot compel the private repositories like Lawphil and Chan Robles to remove or delete their names because the information contained in such decision are covered by the right of the people to infoormation on matters of public concer. The right to privacy should be overridden by the greater right to information by the public.

Can we as ordinary citizens create our own version of WikiLeaks and expose anomalies in the Government?

The constitution provides that the right of the people to information on matters of public concern shall be recognized. Access to official records, and to documents, and papers pertaining to official acts, transactions, or decisions, as well as to government research data used as basis for policy development, shall be afforded the citizen, subject to such limitations as maybe provided by law.
Clearly, disseminating factual information for the nation to digest is not a crime but in fact a requirement under the ultimate law of the land. The wikileaks may thus be an allowable means subject to certain limitation as provided by the law. The problem however is that the limitation is not clear this is one aspect where jurisprudence and law has to evolve. The freedom of Information Bill is presently being debated which is hoped as a solution.
In the case of Asange, qouting time dated December 9, 2010 wherein the weakness of the case against Asange himself was evident. There is no law in th US that punishes the act.

"But the law is too broad a brush to try to draw a distinction between WikiLeaks' indiscriminate posting of the cables — which Burns called "nihilistic" — and the more careful vetting evidenced by The New York Times, Abrams said. How do you draft a law that targets WikiLeaks but leaves intact our system of press freedoms? "It's very difficult to do," Abrams said. Besides, he said, "the courts have never required responsibility as a prerequisite to press freedom. That's never been the legal standard." In addition, claims that Assange has simply dumped the documents without reviewing them, much like a traditional editor would, have been disputed. Assange himself told TIME that each diplomatic cable his site has published has been vetted by his own team or by the editors of newspapers with whom he has shared the documents."

Relatively, whether Assange case will prosper is relavant in this issue and it will surely affect future laws and jurisprudence in the Philippines.