A server can be programmed to do anything yes. if a hacker can get access to a server, he/she could re-program it, yes
"doing it by proxy." is probably not the right thing to say in this context as Internet proxies are simply intermediaries that pass on information between two communicating systems
You could say that a temporary ISP does exist, in the context of a customer relation, but not in terms of the Internet, it requires stability. So an ISP can act a s a temporary provider to a customer, but not to the bigger ISPs that it plugs into to provide a service to customers
