There are 4 pages of allowed foods in the DANDR book. If a food isn't listed on those 4 pages then it isn't allowed.

The reason behind induction is to help break the addiction to carbohydrates. You can not do this by consuming sugar free candies, jello etc etc.

He allows you 3 artifical sweeteners a day. Period. No exceptions. After you finish induction, you can have things in moderation provided they do not cause cravings or insulin spikes.