Why does the AI have blueprints to the SR2?

No. I would rather they fit the Tempest with a weapon somehow rather than the Normandy return. I like the Tempest and don't want to see it go. Besides that, I would feel slightly cheated to have a Normandy lookalike return without Shepard and company to fill it.. Just leave the past in the past. This is all new!

I think it's mostly as an easter egg than anything else.. Although there is speculation that the Benefactor for the Andromeda Initiative could have ties to the Illusive Man or Cerberus in general so if that's the case, it would make sense that blueprints for such an advanced ship would come along to a new galaxy.

I have bigger issues with the SR2 being displayed in the Pathfinder room than the SR1. They clearly label the SR2 as a Human/Turian designed ship even though that was clearly not the case. What makes this even more baffling is that the first Normandy was actually reported on by Khalisah al-Jilani! So a ship that was built in secret by a pro-human group gets more attention than the one that got actual press attention and who's destruction was known pretty much throughout the cosmos. I just don't get it. Did someone on the design team just hate the original Normandy that this was their way of eliminating it from canon?

It was intentional. I vaguely seem to recall that the devs mentioning in an interview that they wanted the Tempest to feel like it was drawn from the same design-lineage as Alliance vessels, but the design they ended up with looked too much like the Normandy.

So they decided to flip the model upside and alter the wing-fins.

Actually when you think about it, the Tempest not having a gun ended up being a blessing in disguise.

The Angara would likely have never let the ship land on Aya if they'd detected it was armed to the teeth. To preserve the secrecy and safety of their people, they'd have probably been very justified if they'd blown the Tempest out of the sky, fearing it posed a threat to them.

Whereas the Tempest being unarmed meant they could risk letting it land. If those onboard did end up being hostile, they could easily imprison the crew and impound the vessel to keep the location of Aya secret.

Trying to find that interview, but it's proving illusive. Anyone else remember where they said this, did I imagine it?

I know that Joel Macmillan helped design the look of it. Also that one of the rejected concepts was for the cargo bay to be at the top, so that the Nomad would drive on the roof and down the nose of the ship, which would bend (somewhat like a Concorde) to form a ramp.

I agree that the SR1 would've been a better choice. I suspect that they figured more players would be familiar with the SR2. The fact that the SR2 was more advanced may also have played a part.

The SR2 is a Human/Turian design, though. It's derived from the SR1, to which Cerberus provided some early impetus. TIM then had his engineers design a better, less budget-restricted version for the coming war. (This is one of the few instances involving Cerberus that actually made sense, given their Alliance ties and Cord-Hislop.)

As to the question posed by Andrew Waples in the OP, it's bluntly hinted that they stole the prints, or at least obtained them illegally. "Top Secret" doesn't mean completely untouchable. There's always a way with greed in play. We don't know who the true backers of the Initiative were, but the SR2 prints aren't even the craziest thing with which they got away. They developed multiple AIs, vessels that are dreadnoughts sans guns, etc... Clearly, a lot of exceptions were made for this project. The Initiative must have had powerful backers in the highest levels of government.