Weight and inches loss question

It's funny because I've been reading these boards for a few months now and I'm still as confused about this.

First, weight loss isn't linear. I got that part. For the last few months, I only lose weight one week a month, typically 4-6 lbs at a time (2 of water weight from the previous month, and a few extras). So, question... what happens during the other 3 weeks when I'm still eating at a deficit but the scale doesn't move (or moves up a bit)? Surely if I'm eating at a calorie deficit, I should burn fat, right?

Second, the whole 'you might be losing inches but not weight' thing... how is that even possible if you can't build muscle on a calorie deficit?

Really trying to understand it.