Am I doing this right?

GoalWeight165by2018

I have about 40 lbs to lose. I'm eating a calorite defecit, enough for a 1 pound loss per week.
I work out at a class at the gym M - F 545 to 645. The class does one minute of cardio, then one minute of strength, for the duration of the class. I wear the fitbit, which adjusts my calories for the day (and I have turned on the negative adjustment part, too,). I eat back most of those calories, save for 100 - 200 a day, which I dont' eat back.
I am losing weight and feel fine.
But, specifically, here is what I am worried about:
Working out while in a calorie defecit, especially if I eat back the calories, does that help me in any way?
Do I have to lose fat before I gain muscle? Am I sort of doing them both at the same time with the strength + cardio class?
Is it necessary to take days off between teh workouts?
Thank you!