Technology has surpassed the need of an government agency to deliver slips of paper wrapped in other slips of paper to every house in the country, and the only reason their package delivery is up is because of the internet.
This is true, but its also important to point out that the USPS is only a government agency in name. They are entirely self-sufficient and not supported by tax dollars. The only benefit they get to being a government agency is the ability to put mail into a box that is required to be installed on your property (or, in most new neighborhoods, in a collection of boxes somewhere down the street).
No, they're a government agency pretty much all the way since they're governed directly by Congress. This entire weekend off proposal isn't going to happen unless Congress approves it.
Also: they're in the constitution.