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两个全等的三角形ABC和DEF重叠在一起,△ABC的面积为3,且AB=CB,固定△ABC不动,将△DEF进行如下操作:

两个全等的三角形ABC和DEF重叠在一起,△ABC的面积为3,且AB=CB,固定△ABC不动,将△DEF进行如下操作:
(1)如图①,△DEF沿线段AB向右平移(即D点在线段AB内移动),连接DC、CF、FB,四边形CDBF的形状在不断地变化,但它的面积不变化,请求出其面积;
(2)如图②,当D点B向右平移到B点时,试判断CE与BF的位置关系,并说明理由;
(3)在(2)的条件下,若∠AEC=15°,求AB的长.
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