I picked these points as they're space-related
"Why do many moons in our solar system still have magnetic fields? They should have cooled off inside after several billion years, and the molten core is necessary for a magnetic field?"
The major moons of Jupiter are very hot at their cores because they are constantly being squeezed and expanded as they go round the planet (imperfect orbits and the huge mass of Jupiter cause these effects). This is why Io is more volcanic than Earth. I don't have a list of all the moons of the solar system and how strong their magnetic fields are (and for some reason I can't access Google!) so that's my suggestion for now.
"How accurate can interstellar measurements be? The base of our triangle used for parallax is 16 light-minutes, and we're somehow accurate out to millions or billions of light-years? The angle at the tip of the triangle for a star 1 light-year away is .017. For 100 light-years away, it's .00017, and so on. 100 light-years is like two people 16 inches apart trying to measure ~800 miles away--the room for error is immense."
Actually, a lot of distance measuring is done by classifying stars. If a star is a certain shade of blue that tells you roughly how hot its surface is and by comparing how intense the light from it is to the amount of light we'd expect to be radiated off the surface (look up black body radiation) an estimate of the distance is possible. For huge distances (i.e. to other galaxies), astronomers look for supergiants, variable stars etc. to use as a yardstick. Parallax is only used for very close stars.
Don't forget we're not using our eyesight to judge distances, but augmenting our vision with powerful telescopes, many of which are automated and don't even bother looking in the tiny visual part of the EM spectrum.
Oh, and if several people tried measuring the 800 mile distance standing 16" apart every night for a month and the average of the sensible (you'll always get the odd freak result, which is why you take measurements more than once) results came out as pretty close to 800 miles, would you credit it or simply assume they'd cheated?