Wire-to-turnbuckle size

[Brion Toss]

Oy,
First, I think it is safe to disregard the hardware store clerk as a source of reliable engineering data. Next, as noted in the previous post, the standard SF for industrial gear is 5:1, though who knows what standards these shackles will meet; the catalog for this specific brand should provide that info. Next, galvanized shackles always have a pin one size bigger than the bail. The diameter is measured at the narrowest portion of the bail, just above the eyes. The way that the loads are distributed this makes sense (stainless yacht shackles often have bail and pin of the same size, but this has to do with shackle design and use).
Next, partly because of loads needing to turn corners, and partly to assure that turnbuckles and shackles are appropriately stronger than the wire they hold, wire will always be smaller in diameter than the other hardware.
All of this has been worked out by centuries of people breaking stuff, figuring out why it broke, and finally coming up with appropriate standards. If you want to understand the reasoning behind those standards (and I recommend it) the resource materials are widely available. But it might be enough for you, and far simpler, simply to adhere to the standards. I can recommend my book as one source of sizing information. Also Skene's, Larsson and Eliasson's, and others.
Can't help you with the propane fitting anomaly, but it seems a poor bet to assume there's no hard-won logic there, just because it isn't obvious to you.
Fair leads,
Brion Toss