1. Why should we consider the "correct" adult grammar as a subset of the child's "overly general grammar"?
The child understands the correct forms, so these must be part of the child's grammar.  But the child also produces nontargetlike forms, showing that the child's grammar is larger than the adult's.

2. Why do we place "goed" in the outer set, and "went" in the inner?
"Went" is the correct (irregular) past form of the verb "go."  It therefore belongs to the "correct" grammar.  "Goed" is a nontargetlike past form frequently used by children as they acquire the English past.  It is formed by regularising the verb "go," and so applying the past rule add -ed in too many contexts, i.e., overgeneralising.

3. How does a child learn to reject the incorrect form "goed" and accept only the correct form "went"?
(HINT: read L2 past and Connectionism)

Emergentist theories like MacWhinney's Competition Model explain the child's recovery from overgeneralisation errors like *goed by reinforcement in the input: the correct form went is reinforced each time it is heard in the input, while the incorrect *goed is never heard and thus dies out.

4. How would a UG theorist explain the same phenomenon?

Universal Grammar posits that children's grammars are innately constrained: we are pre-programmed not to make certain errors.  The emergentist position, articulated here by MacWhinney, claims that we do not need to include such innate constraints in our model of child language acquisition:

"Evidence that the child follows some general guidelines in recovering from overgeneralization and avoiding errors can be interpreted as evidence for innate constraints. However, it can equally well be explained through the operation of emergent constraints that solidify during the process of language learning itself. In other words, the child can use language learning to learn about the shape of language learning."            (MacWhinney, 1996)