1. The first question is the application of congruent triangles. For right triangle ABE and right triangle ADF, AE = AF and AB = AD (HL), so △ Abe △ ADF, that is, BE = DF.

2. The quadrilateral AEMF is a diamond,

Because △ Abe △ ADF, ∠BAE = ∠DAF, ∠CAE = ∠CAF, because AE = AF, AO = AO, △ AFO △ AEO, OE = OF, ∠ AOF.

I hope my answer is helpful to you.