The brompton mudguards are Nisna, they stopped making them. The Bime Friday are recently custom made by Woody's Custom Fenders. They are gorgeous IMO. I have 2.25 inch studded tires on in the winter that the stock fenders were no Bueno for.
Oh yeah, my rear cog on my bike friday was skipping, and I couldn't personally get it quite right, so off to the shop it went. Chain is still good.
I had a similar issue on my full size bike and it turned out the cable had corroded. It took a bit to figure out because after the shop tuned it it would work fine for 100-200 km or one tough climb but then start skipping again.