I have a few questions about BMR and losing weight.

I have a BMR of ~2000 (give or take 50). I had a Inbody test done, I'm assuming this is accurate. I've been told this is the coma calorie rate. If your in a coma, this is the number of calories you need to not waste away and thus about 60% of your actual caloric needs. I'm also 42% body fat and ~100lbs overweight.

I want to drop that to into the 12-15% range and just lose the pounds over the next 14-16 months for dovetail reasons.

Originally, I was at 1500 cal a day. I was eating when I was hungry, not till I was full, yada-yada. It was pointed out to me that I wouldn't be able to build muscle under those circumstances so I bumped up to right at my BMR to keep skeletal muscle mass etc. I gained three pounds this week at weigh in. So my question is how, because I'm obviously still in a calorie deficit. My hamster wants to believe I'm converting fat to muscle but I'm not quite buying it. Is this normal? Am I fucking something up. Tips from those who have been on this journey appreciated.

Edits: Spelling, etc.

Edit 2: Since there seemed to be some confusion, I wanted to make it explicit that I am lifting 3-4 times a week. (Modified Stronglifts 5x5 until my core is strong enough to support weight around a bad disk) I'm also 23