Determining Vo in a diode circuit using iterative analysis
No, you're asked to find the output voltage within a tolerance of 15mV.

See above.

Initial assumption doesn't matter too much, it saves iterations if you are closer. If you assume a current (it will be fairly low in this case, maybe uA for a silicon diode), then calculate Vo, then you'll have a new current based on (1V-Vo)/R1. Calculate Vo again, repeat until it converges well enough.