(2) established.

Because CE=DF, CD=AD, angle ECD and angle ADC are equal (square), triangle ADF and triangle EDC are equal, AF=DE is deduced.

Because angle DEC and angle EDC are complementary, and angle DEC and angle AFD are equal, and angle AFD and angle EDC are complementary, angle DGF is 90 degrees, that is, DE is perpendicular to AF.

(3) square.

Because points M and Q divide AE and AD equally, in a triangular AED, MQ parallelism is equal to half of ED according to the midline theorem. Similarly, PN parallelism is equal to half of ED, so MQ parallelism is equal to NP.

Similarly, it can be proved that PQ is parallel and equal to MN,

And AF is perpendicular to ED, PQ is parallel to AF, MQ is parallel to ED, so PQ is perpendicular to MQ,

To sum up, quadrilateral MNPQ is a square.