$证明:(1)∵DE//AC，CE//BD，$
$∴四边形OCED是平行四边形.$
$∵矩形ABCD的对角线AC、BD相交于点O，\ $
$∴AC=BD，OC=\frac{1}{2}AC，OD=\frac{1}{2} BD，$
$∴OC=OD，∴四边形OCED是菱形.$
$(2)∵四边形ABCD是矩形，BC=3，DC=2，\ $
$∴OA=OB=OC=OD，S_{矩形ABCD} =3×2=6，\ $
$∴S_{△OCD} =\frac{1}{4} S_{矩形ABCD} =\frac{1}{4}×6=1.5.\ $
$∵四边形OCED是菱形，$
$∴菱形OCED的面积=2S_{△OCD} =2×1.5=3.$
