By Dan Levine (Reuters) -Democrats in the U.S. Congress proposed a raft of new rules for the federal judiciary on Wednesday including a formal mechanism to remove judges from hearing cases in the event of a conflict of interest and another intended to reduce secret court filings. The legislation was being introduced in both the House of Representatives and the Senate. Among its sponsors are House Judiciary Committee Chairman Jerrold Nadler and Senate Judiciary Committee members Sheldon Whitehouse and Richard Blumenthal. The bill comes as U.S. Supreme Court Justice Clarence Thomas has faced cal…