(1)椭圆x²/5+y²=1①的上顶点C为(0,1),
设直线PQ:y=kx+m,②代入①,x^2+5(k^2x^2+2kmx+m^2)=5,
整理得(1+5k^2)x^2+10kmx+5m^2-5=0,
设P(x1,y1),Q(x2,y2),则x1+x2=-10km/(1+5k^2),x1x2=(5m^2-5)/(1+5k^2),
由②,y1y2=(kx1+m)(kx2+m)=k^2*x1x2+km(x1+x2)+m^2,
y1+y2=k(x1+x2)+2m,
由CP⊥CQ得x1x2+(y1-1)(y2-1)=x1x2+y1y2-(y1+y2)+1
=(1+k^2)x1x2+(km-k)(x1+x2)+m^2-2m+1=0,
∴(1+k^2)(5m^2-5)-10km(km-k)+(m-1)^2*(1+5k^2)=0,
整理得10（m-1)=0,
∴m=1,此时直线PQ过定点C,但是不满足CP⊥CQ,∴不存在满足题设的PQ.
(2)F(2,0),设AB:x=ny+2,③交y轴于点M(0,-2/n),
把③代入①,n^2y^2+4ny+4+5y^2=5,
整理得(n^2+5)y^2+4ny-1=0,
设A(x3,y3),B(x4,y4),由向量MA=a向量AF,向量MB=b向量BF得
(x3,y3+2/n)=a(2-x3,-y3),(x4,y4+2/n)=b(2-x4,-y4),
∴a+b=(y3+2/n)/(-y3)+(y4+2/n)/(-y4)
=-2-(2/n)(y3+y4)/(y3y4)
=-2-(2/n)*(-4n)/(-1)
=-2-8=-10.