1. Problem: A disappearing language
The New Media solution would be option B. Option B distributes information to many people instead of keeping them to themselves. This is the better solution in the long run so that the children can share all the stories and create an online dictionary instead of a one-to-one solution. This is also my preferred choice.
2. Problem: Neglected ruins
Solution B would be the New Media solution. Leaving a bread trail letting other adventurers where people have already been and maybe some information about the place creates a database. You can then go behind that person and maybe add anything they may have missed. This is Many-To-Many.
3. Problem: Misunderstanding computer animation
While neither of the solutions are really Many-To-Many, I feel as though solution A would be more New Media solution. For example, you are in the museum, you can pick what you want to look at and what you want to see, while observing the real thing at the same time. Solution B does not allow you to do this.
4. Problem: A broken fountain
The New Media solution to this problem would be Solution A. It would be solution A because it involves bringing together many people to create a solution to a growing problem. Networking a bunch of different clubs and facilities to come together.