Sign across resistor, circuit with diodes and fuse
Edit: Apologies, I misread the polarity they'd given. Yes, this is wrong. The plus and minus signs on Rl are the wrong way round. Other than that, their working is correct.

No. As long as you're consistent, and you stick with the passive sign convention, it doesnt matter what direction you choose to represent your current. In this case, everything in their working seems correct.