As much as you want!

The first phase you are expected to lose anywhere between 8-13 pounds in the first two weeks. The second phase does not have a time limit. You have a target weight and you continue until you reach that target weight, if you begin to gain weight during phase 2 or no longer lose gradually then you cut back of fats and simple carbs. Phase three only begins after you lose all the weight you want and its there to stabalize your weight and make sure you don't gain things back.

I'm about to start the second week of Phase 1 and I have only lost 1 pound! What am I doing wrong?

You are probably doing everything right, I'll assume you are following the diet and exercise plans of course.

Phase 1 is not the phase for weight loss. If you do lose weight then it will be water weight, and you may just not have that much to lose in terms of water weight.

The point of phase 1 is to curb your cravings, most weightloss will happen in phase 2, so don't worry!

Good luck with your diets!