(1) According to the meaning of the question, E = CA = 32, c2=a2-b2, while a=2b and c=3b.

So A(0, -b), F(3b, 0),

So the equation of the straight line L is: x3b+y? B = 1, that is, x-3y-3b=0,

Because the straight line l and the circle c: x2+(y? 2b)2 = 274° tangent,

So |0? 23b？ 3b | 2 = 332，b= 1，a=2，

So the equation of ellipse E is: x24+y2 =1;

(2) When PQ, CP and CQ are connected, there is |PQ|≤|CP|+|CQ|=332+|CQ| (if and only if P, C and Q are collinear and P and Q are not normal in C).

So when |CQ| takes the maximum value, |PQ| takes the maximum value.

Let Q(x0, y0) give x024+y02 = 1,

C (0 0,2), then |CQ|=x02+(y0? 2)2=4? 4y02+(y0？ 2)2=? 3(y0+23)2+283，

Because y0 ∈ [- 1, 1],-1

Put y0 =? 23 is substituted into x24+y2 = 1, and x0= 253 is obtained.

Therefore, when |PQ| obtains the maximum value, the coordinate of point Q is (253, -23).