As shown in Figure 1, there are a pair of triangular plates, in which ∠ B = ∠ E = 90, ∠ A = ∠ C = 45, ∠ F = 30 and AC = ef = 2. Two triangular plates ABC and DEF are stacked together (Figure ②).

(1) When the rotation angle is 45, what is the quantitative relationship between EG and AB?

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(2) When DF passes through the vertex B of triangle ABC, find the degree of rotation angle α.

(3) Is there a point P on DF that makes ∠ APC = 90 when triangle DEF rotates around point O? If yes, please draw this point on DF with a ruler and compasses and explain the reasons. If not, please explain why.

(4) Take a point m on the ray EF, and the parallel line passing through m as DF intersects the ray ED at point n (as shown in Figure ④). If there are always two points P and Q on the straight line MN, so that ∠ APC = ∠ AQC = 90, find the value range of EM.

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