NEW YORK, Feb 23 (Reuters) - Sarah Palin, the former Alaska governor and 2008 Republican U.S. vice presidential candidate, plans to seek a new trial and have the judge disqualified after losing her defamation case against the New York Times. U.S. District Judge Jed Rakoff in Manhattan discussed Palin's plan at a hearing on Wednesday, and said he will issue a written opinion by March 1 explaining why he dismissed her case while jurors were deliberating. He said he would speed up the opinion because of the "fracas" surrounding the dismissal. The unusual hearing came eight days after jurors rejected...