By Saqib Iqbal Ahmed NEW YORK (Reuters) - The U.S. dollar fell to a fresh four-year low against the euro before reversing losses to trade higher on the day in a choppy session after the Federal Reserve cut interest rates by a quarter of a percentage point. The rate cut, along with projections showing two more quarter-percentage-point reductions are anticipated at the remaining two policy meetings this year, indicates Fed officials have begun to downplay the risk that the administration's trade policies w ...