The short answers are:

1. No, it doesn’t really work.
2. It is rather unhealthy, although IIRC it’s main plank is many hours of sauna and massive doses of vitamins.
3. Maybe – maybe not. It’s unlikely that Narconon would treat for a skin condition – whether or not they would prevent use of medicated cream depends on the official in charge. Narconon – as a branch of scientology – has peculiar views on medication, and will try to stop people using anything they consider mind altering – this can include painkillers.

For analysis of Narconon:
http://www.cs.cmu.edu/~dst/Narconon/
in particular: http://www.cs.cmu.edu/~dst/Narconon/doesitwork.htm
and: http://www.cs.cmu.edu/~dst/Narconon/safety.htm

There are concerns about Narconon’s safety. I’ve seen at least one Answerer here who had a bad experience with Narconon, and hopefully you’ll get to see her views for yourself.

Be aware that Narconon is a front group for scientology – it uses scientology doctrine and there may be pressure to join the cult.