Advice on Fitness Routine

Ok, so I revamped my fitness routine 2 weeks ago and was hoping to get some additional feedback. I started training with a trainer (weighlifting) for 3 days a week. We have 30 minute sessions where I lift with VERY little rest betweens sets and exercises. I do a different body part each day--Legs (Mon), Arms(Wed) and abs/back (Fri). After working out with him, I do at least 30 minutes of cardio on Monday and Wednesday (sometimes Friday). On Tuesday, Thursday and Saturday, I do 45-60 minutes of cardio. I've been taking cardio bootcamp/kickboxing classes or doing the treadmill for an interval workout (not HIIT). I upped my calories to accomodate my workouts. So, I try for 1650-1750 cals a day (1000 calorie deficit). I did lose about 1.8 lbs last week (for a total of 40 lbs). But, I want to know if this is sufficient to build muscle and lose fat?

bump!