I hate to ask a question against a question, but is the diet that has you eating ~500 calories while taking injections or pills/orals of some sort?
There have actually been a few studies done and the HCG actually does not do anything concerning the weight loss. The weight loss happens from restricting calories dangerously low.
To answer your first question I'm not too fond of this because 1) the practioners of this so called diet got their asses handed to them by the FDA, and 2) this is probably one of the most efficient ways to destroy your metabolism VERY quickly.
To answer your second question, depending on your wife's goals would be the training protocol she would take. I'm guessing she wants to slim down, maybe add some appreciable amounts of muscle. She could do:
*Hard body training for women
*female complexes for fat loss
You can look these up on this site
She can also do:
* a 5x5 program
Just get her eating a reasonable amount of calories to sustain growth, have her throw in some conditioning maybe two times a week, and be patient, and throughly do your research, but please get her off of that diet.