What are these connectors? And how can I connect to them with my own stylish red hoses?
These are SRAM inline hydraulic hose connectors, an article on Bikerumor mentions these are supposed to be OEM only:


  We mentioned that the new Connectamajig will be offered for use with
  this, and it’s aimed at the OEM manufacturers to ease assembly line
  efforts. SRAM’s product managers were careful to point out that it’s
  not really designed to be a quick disconnect for travel frames, it’s
  primarily to make installation easier.




If you look at photo above, you can see the male part, so I'd look around for it. Also, if you are building a brand new Specialized out of the box, I'd try to connect their customer support or wherever you purchased the bike from for assembly advice.