Yes, you can eat honey and other allergenic things like nuts when bf, but advice is not to give to baby. Of course if there is any sign that bf baby is reacting to these in your diet, may be worth to speak to someone about your diet.
Yes, you can diet. Kellymom.com gives an excellent guide - she says don't eat less than 1500 - 1800 calories per day when dieting. That is about 300 - 600 cals. more than someone not bf.
Weight Watchers allow you to eat a few extra points (I think it is 5 extra points per day) when you bf an infant under a year old.
Good luck !