For those possessing limited knowledge of proof assistants, I recommend this article in Quanta Magazine as an approachable introduction. https://www.quantamagazine.org/building-the-mathematical-library-of-the-future-20201001

One of the best solutions I have used employs a shared desktop to use design tools. I've done this with VNC. "Sharing the mouse driving" actually seemed pretty natural. And it's cheap and simple. It does require some politeness though, and low network latency - a plus anyway. I have to add that I have only done this with a group of two. I don't know how it scales.

Answer: Those who are plugged into a power outlet and can charge (or get some sort of credit) for the service.

Most of the MANET routing stacks provide for optional routing anyway. So, if you don't want to forward for someone else, don't.

There has been a lot of work done on MANETS. Just search almost anywhere for "mobile ad hoc networking". Wikipedia has a short article that looks like a good starting place for a beginner.