the second question

Connect AM and cross ED at o.

∫S△ABM = S△ACM = 1/2S△ABC

Ae is parallel to DM

∴S△AED=S△AEM

AOD = EDM

∴S△AMC=S△AOD+S quadrilateral ONCD=S△OEM=S quadrilateral OMCD= 1/2S△ABC.

∴DE divides the area of △ABC equally.

Third question

Connect BD and AC, take the midpoint m of BC, connect CM and AM, make a straight line parallel to AC after passing AM, and connect AE at point E through BC.

Then the straight line AE is the expected straight line.

(If it is not proved, you can push it according to the second area. )

Tip: the distance between parallel lines is equal everywhere, and the equal base and high area of a triangle are equal.