I'm not certain, but evidence suggests Favor affects per-sector ratings. Higher favor correlates with higher ratings. I wonder if that stat also affects ratings for the whole run? It's hard to tell, but ships with higher stats certainly seem to get better ratings when exploring only earlier sectors.

I strongly doubt that the airship condition message has anything to do with the repair level of the airship, but I have no evidence to back this up. But, nothing else in the game works like that - combat gear doesn't do less damage or give less defense when near to breaking. Damaged crafting gear doesn't decrease the number of Goods you get or anything. It's all all-or-nothing. Also, plenty of weirdly worded messages pepper airship logs. Like, the no wind message mentions surveillance, but the surveillance stat doesn't correlate with better weather. Heck, I don't even see a correlation between retrieval level and retrieval rating despite it having retrieval in the name... That one needs more data, but it's almost like the higher your retrieval, the more items you get, independent of the rating shown.

As for how finding a second item works, I like the theory of "airship HP" mentioned earlier. The idea being that the airship starts each sector with a set amount of HP (likely based on some stat), and wind reduces this HP, as does the first retrieval. The "damage" from retrieval is likely based on the sector's rating. The "damage" from the second item's wind+retrieval is compared to the ship's remaining "HP" and, if the damage is higher, you fail to get a second item. If your ship will be above 0 after the "damage," you get a second item. The HP then resets for the next sector. If that theory is correct, the "airship condition" message makes total sense.

Of course, I have no idea how to prove or disprove that theory.