Actually for the first part, there is this protocol called SDCH (https://en.wikipedia.org/wiki/SDCH) that allows a site owner to define a site-global compression dictionary, and each resource then becomes a compressed resource with the dictionary being the former one. It's hard to deploy, but it works: LinkedIn saw an average of 24% additional compression.

For the second part I wonder if browsers could display stale data with some warning saying so; that would solve many problems that happen all the time (refreshing a page after the website came down, ...)