Is it safe to connect a 16-gauge extension cord to a 12-gauge cord using a female-to-female adapter?

No, that’s not safe. The 16-gauge cord is the weak link — it can only handle about 13 amps, so a 15-amp device will overheat it. The female-to-female adapter is also a hazard: it’s often cheap, unlisted, and can expose live prongs. Don’t daisy-chain mismatched cords; buy a single cord in the right gauge for your load.