So ED=AF, EA=DF.

Because ED//AB, because ∠CED+∠AED= 180.

∠CED=∠CAB=∠DFB

∠DFB+∠AFD= 180

So ∠AED=∠AFD

So △AED is all equal to △AFD, so ∠ADE=∠ADF.

And because it is obtained from ED//AB, ∠EDA=∠DAF (internal dislocation angles are equal).

So ∠DAF=∠ADF, so AF=DF, so DF=DE, so ∠DEF=∠DFE, so △DEO is equal to the triangle DFO, which proves that DO shares △DEF equally.

There is something wrong with the second question. What do you mean by exchange? I don't understand.