@Dreikin said in Alice through the Effin looking glass:
Also works as a sentence in response to a question such as "which ball?".
Neither of those is a sentence; they are both sentence fragments. The context implies the missing parts of the sentences ("Which ball [do you want]?" "[I want] the ball John gave Jane."), but neither is a grammatically complete sentence as written.
@Dreikin said in Alice through the Effin looking glass:
This works perfectly fine as a sentence.
Grammatically, yes, but semantically it's nonsense; the subject cannot perform the stated action.
@Dreikin said in Alice through the Effin looking glass:
Also works as an answer (with some punctuation). "He did what?" "Gave John the ball "Jane"".
Again, it is not a complete sentence as written. It requires the context to imply the subject he. It also requires context to supply the information that Jane is the name of the ball; without that, a reasonable reader would assume Jane is a person who is somehow involved with the action of the sentence, but it is very unclear what her involvement is. Also, the punctuation really isn't optional. "This is my wife, Jane." "[He] gave the ball, Jane [, to implied indirect object — give is generally used transitively unless the indirect object is pretty clearly implied by the context]."