解：（1）因为$\angle ACB = 90^{\circ}，$$CD$是高，所以$\angle B+\angle CAB = 90^{\circ}，$$\angle ACD+\angle CAB = 90^{\circ}，$
所以$\angle B=\angle ACD。$
因为$AE$是角平分线，所以$\angle CAF=\angle DAF。$
因为$\angle CFE=\angle CAF+\angle ACD，$$\angle CEF=\angle DAF+\angle B，$所以$\angle CFE=\angle CEF。$
（2）因为$\angle B = 40^{\circ}，$$\angle ACB = 90^{\circ}，$所以$\angle BAG=\angle B+\angle ACB = 40^{\circ}+90^{\circ}=130^{\circ}。$
因为$AF$为$\angle BAG$的平分线，所以$\angle GAF=\angle DAF=\frac{1}{2}\times130^{\circ}=65^{\circ}。$
因为$CD$为边$AB$上的高，所以$\angle ADC = 90^{\circ}，$所以$\angle CFE = 90^{\circ}-\angle DAF=90^{\circ}-65^{\circ}=25^{\circ}。$
又因为$\angle CAE=\angle GAF = 65^{\circ}，$$\angle ACB = 90^{\circ}，$所以$\angle CEF = 90^{\circ}-\angle CAE=90^{\circ}-65^{\circ}=25^{\circ}。$
（3）因为$C，$$A，$$G$三点共线，$AE，$$AN$分别为$\angle BAC，$$\angle BAG$的平分线，
所以$\angle EAB=\angle EAC=\frac{1}{2}\angle BAC，$$\angle NAB=\frac{1}{2}\angle BAG。$
所以$\angle EAN=\angle EAB+\angle NAB=\frac{1}{2}(\angle BAC+\angle BAG)=90^{\circ}。$
所以$\angle EAM = 180^{\circ}-\angle EAN = 90^{\circ}，$所以$\angle M+\angle CEF = 90^{\circ}。$
因为$\angle CEF=\angle EAB+\angle B，$$\angle CFE=\angle EAC+\angle ACD，$$\angle ACD=\angle B，$
所以$\angle CEF=\angle CFE。$
所以$\angle M+\angle CFE = 90^{\circ}，$所以$\angle CFE = 90^{\circ}-\angle M=90^{\circ}-35^{\circ}=55^{\circ}。$
