* U.S. shares rise, lifting global index* Dollar index rebounds, euro hit by German data* Oil falls further, IEA revises down demand growth forecast(Recasts throughout, updates prices, changes byline, changes dateline from previous LONDON)By Rodrigo CamposNEW YORK, Oct 14 (Reuters) - A rebound on Wall Street buoyed global equity markets on Tuesday, but lingering anxiety over world economic growth