Will a 2.2 ecotec motor out of 2007 cobalt fit the mounts 2004 cavalier with same motor?

No, a 2.2 Ecotec motor from a 2007 Chevrolet Cobalt will not fit on the mounts of a 2004 Chevrolet Cavalier with the same 2.2 Ecotec motor. There were significant changes to the Cobalt platform for the 2005 model year, resulting in different engine mounting points. Therefore, the Cobalt ecotec will not mate properly to a pre-05 cavalier transmission.