Hypothesis of communication In the first example it seems likely that a new language would be developed with elements of each individual's own languages. I am not entirely convinced that the different types of language stated are so distinct. Initially I think that the most easily transmissible language would develop which would most likely be basic hand gestures. At this early stage this language would also possess the greatest utility considering it would not yet be possible to develop a more efficient means of communication. For me it seems unlikely that the group would collectively decide to use a particular individual's language since they would have no basis to make such a decision. Therefore I don't think it would be possible to choose a group member to teach the rest their language.
In the second example, I think it needs to be specified that the group do not share a common language and that the teacher does not speak any of those languages. In this context, for me 'group' implies that they do share a common language which the teacher does not speak. If the group did share a common language, the process of learning 'Speakanese' would most likely be a lot faster given that the group could communicate with each other and reach some agreement on what the teacher is referring to. However I agree that no matter if the group shares a common language or not, the group's understanding of 'Speakanese' will always be imperfect.
Additionally, as far as I know in other languages there are certain words that are literally untranslatable in to other languages without losing meaning. I'm afraid I don't know any specific words but might be interesting to explore in this example.