What are the dimensions of an NPT pipe for fuel systems?
Mechanical engineering uses a particular wording, I hope I'll not lose myself in the translation... Feel free to correct.

This fitting, standardized in ASME B1.20.1, has the particularity to have conical nut and screw:

  

The thread is tapered:


Larger diameter ($\small \rm E_2$) = 1.00178 in
Smaller diameter ($\small \rm E_0$) = 0.96768 in
Effective length $\small \rm L_2$ from $\small \rm E_0$ to $\small \rm E_2$ = 0.5457 in


1) How do I decipher the specified pipe size? This one is 3/4

Difference in diameter over $\small \rm L_2$ = 0.0341 in. As $\small \rm L_2$ = 0.5457 in, this is equivalent to 0.75 in per foot (12 in) or 3/4 in/ft.

This is where the size 3/4 comes from. 

2) Why would the unthreaded side have the diameter 1.050 in? I want to connect it to a pipe with a 1.0 in

When fully engaged, the screw thread and the nut thread are fully adjusted. The extremity of the screw is at the reference plane (see figure), and the nominal diameter is $\small \rm E_0$

$\small \rm E_0$ is smaller than $\small \rm E_1$, the diameter at the extremity of the nut, both are smaller than $\small \rm D$, the external diameter of the screw.

For a threaded screw, the "diameter" is often the diameter of the unthreaded rod, this is also the case here $\small \rm D$ = 1.05 in.