Looking closer at my BNC patch cables they are 75 ohm not 50 ohm. How does this effect the signal and reading on the scope?
It means that the transmission line (cable) isn't correctly matched to the function generator or the scope. This will result in some of the signal reflecting off the point where one joins the other, and as these reflections travel up and down the cable they will interfere with the main, wanted signal. This results in distortion, which you should see on the scope. How bad this distortion is will depend on how fast the edges of your square wave are, the length of the cable, and the bandwidth of your scope.
Here is what I am seeing so far;
1) I connect the 50 ohm BNC to crocodile to the FG then connect the scope probe to that. Voltage measures correctly but the signal is noisy.
Not surprising. Crocodile clips aren't controlled impedance, ie. they're not 50 Ohm, or 75 Ohm, or anything else which can be reliably stated. Expect distortion which varies depending on how the clips are attached.
2) I connect the 75 ohm BNC patch directly from the FG to the scope. Signal is clean but measured voltages are high.
That's odd, the voltage should be about the same, since all you're doing is changing one cable for another. Set the function generator to a low frequency, so transmission line effects aren't important in determining the amplitude of each pulse once it's had time to settle, and try again.
Also check, are you using a 10:1 scope probe but then replacing it with a cable (which, of course, is 1:1)? That would give you an immediate factor of 10 measurement error.
3) Same connection but activate the 50 ohm termination on the scope. Signal is even cleaner but measured voltage shows even higher.
You change the scope from 1M input impedance to 50 Ohms, and the signal actually gets bigger? That makes no sense at all, something isn't right there. The signal amplitude should drop to about 1/2 what it was before.
Another question is on the use of the BNC splitters. What effects will those have on signal and voltage? What is "50 ohm termination" doing? "grumpydoc" mentioned using a BNC splitter with one output having 50 ohm termination vs us using the 50 ohm termination on the scope.
50 Ohm termination should prevent the signal from being reflected at the point where the cable connects to the scope. It's the same as setting the scope to its 50 Ohm input mode. If your scope has a 50 Ohm mode then you shouldn't need the T-piece and 50 Ohm terminator.