Spare tire issue
pretty sure that is a mistake at that factory. If the spare has never been used you should be able to do some kind of trade at a tire shop or even an RV dealer for the right size and be done with it. Then if you do have to use a spare you don't have to worry about it. Tires need to be the same size, even on a trailer. If not, I would at least make darn sure it will bolt on to your hubs.
I'm guessing that both the 15 and 16 inch are a 5.5" bolt pattern. BUt the only way to know is to measure it or just jack a wheel up and see if the 15" inch fits. Then you know that for sure too. But, as I said, I would much rather swap it out for the proper size.