We don't know that S31 has its own shipyards. It seems to operate largely by suborning other Starfleet personnel and facilities, manipulating events so that they do things that advance S31's goals, even if they don't know that's who they're serving.
That's a very good point. It also seems unlikely they could assemble their own shipyards on their own. It seems more likely Admiral Marcus just created the Vengeance on his own--though, I did note that the crew is private security versus Section 31 or Starfleet. Which means they probably don't have the numbers to crew it.
Especially after Khan's destruction of their base.
I liked the Vengeance an abnormally large amount and wonder if it's unique to the Abramsverse. The idea of a 'Dreadnought-class' vessel larger than regular destroyer-sized vessels would be awesome.
I keep saying, the technology already existed as far back as TNG: "Bloodlines." It's just called a subspace transporter there instead.
I'll have to check that out.