Why does Jonas's mother shake her head about the release of the twin and Father's responsibility for it? What wisdom does hunger provide?These...

I think Jonas's mother shakes her head because she is a sympathetic person and believes it will be hard for Jonas's father if he has to decide which twin to release.  Even though Father says matter-of-factly, "it shouldn't be hard, though...usually it's just a matter of birthweight" (Chapter 14), we know from an earlier conversation in Chapter 1, when Father is telling the family about his concern for Gabriel and his fear that the Committe will release him, that it makes him especially sad to have to release a baby. 

In answer to your second question, when the Committee seeks the Giver's counsel as to whether they should allow birth mothers to have more children, he advises them to consider that famine and even war sometimes result when populations grow too large.  He has the wisdom to understand the devastating effects of drastic population increase because he has experienced hunger (Chapter 14).