Electric use for the client on compressed vs not compressed isn't as clear cut as more/less cpu. You also need to consider the reduction in use of the network interface, since the data size will be smaller. Overall latency could improve as well if the compressed form is meaningfully smaller (depending on the tcp congestion window, just one packet smaller can mean a whole roundtrip time)
No, that's not how it works, you cannot upgrade the routers in real-time without complexity and additional cost. So the cost for transfer is fixed with more latency. But if you subtract bad protocol design and the latency added by the compression/decompression I'm pretty sure you end up with the same deal just more complexity that costs even if you don't see the costs.
Just like wind-power actually competes with nuclear because it take 30 days to wind down a nuclear power plant.
Also data can be compressed with more efficient hardware on the backbone without you having to deal with it.
The biggest cost of the internet is idle things and synchronized CPUs, async. never made it unfortunately.
