Is the 3500 calories equals 1lb really true?

Yes, you are looking at it wrong. Weight loss is not linear. The scale won't automatically show the deficit you've created and a number of factors affect the number you see on the scale.

@synacious she has been at it for 5 weeks... Yes, weight loss is not linear, but she should be seeing more results.

BMR is just what your body burns by existing, calories from things like "getting out of bed and on with your life" are added on top of that to get TDEE, so if your'e eating at a 438 calorie deficit from your BMR, you're likely at much too low a target. Too low of a target to be healthy and stick to the plan long-term that is. Not too low to lose weight. There are a variety of reasons not to eat at an extreme deficit, but "starvation mode" is not one of them, for reasons someone will probably come along to post about shortly.

That said, if you were truly eating only 1150-1359 calories a day you would indeed have likely lost more than 1.8 lbs in five weeks, so it's likely your logging is off. Are you using a a food scale? Are you using accurate logging entries? Are you logging everything, including beverages with calories, condiments, candies here and there, cooking oils?

For comparison, I am 5'4, 140~ lbs, and consistently lose weight at .5-1 lb/week on 1600-1700 calories/day with only marginally more exercise than you report.

The most likely answer here is that you're eating more than you actually think. You're not losing at a terrible pace- slow and steady is a perfectly acceptable way to do weight loss- but you don't want to get discouraged and give up- but it's also likely you would see more weight loss even at a higher calorie goal if you were logging more accurately.

Do you weigh all your food on a food scale and religiously log everything? If the answer is no, then you are probably eating more calories than you think, throwing off your formula.

Yes

Be sure you understand the difference between BMR and calorie goal for the day. You said your BMR is 1597 based on your "height and activity level." BMR is Basal Metabolic Rate= what you would burn laying still in a coma to keep your heart beating and liver working, etc. So unless you are literally not getting out of bed EVER, you should be burning more calories than your BMR. Your TDEE (Total Daily Energy Expenditure) is how many calories you burn by being vertical and moving and is definitely affected by your activity level,and your calorie deficit should be subtracted from that.

On a personal note, I am 5'10" and earlier in this journey I weighed a bit more than you. I was trying to eat around 1200 calories per day for the fastest possible weight loss, and I can tell you I felt HORRIBLE. I was grumpy and constantly hungry and had no energy to do anything but sit. I was not going to be able to sustain that. Then I looked up my BMR and it was almost the same as yours... almost 1600. I did a little reading and decided I didn't like the idea of eating less calories than my body needs to maintain my organ function and upped my calories to about 1650. Guess what? I was happier, I wasn't hungry all the time, I had the energy to move my body and I lost weight faster than when I was starving myself. The additional energy I felt allowed me to burn about 200 more calories per day walking (according to my Fitbit), so that increased my deficit while improving my health a bit. I'm sure others have done perfectly well on 1200 calories per day, but I didn't, and actually had a better result eating more.

So at the risk of confusing the issue, yes, weight loss is about a calorie deficit. Yes, one pound is supposed to equal 3500 calories. However, the math isn't perfect because sometimes our calorie intake is not quite accurate, our exercise burn is often an estimate, if you are a new weight lifter you might be adding muscle weight while burning fat, our weight varies daily based on many factors (how much waste is still in your colon, how much water you may or may not be retaining if you ate a lot of salty foods the day before, if you are weighing at the same time of day dressed the same way, and if female what time of the month it is, etc.), and the list goes on.

I agree with those above who have said that if you aren't weighing and really strictly logging everything, your deficit is likely smaller than you think. Another factor that hasn't been mentioned is the quality of the food database entries you are picking. Just because someone else put something in the MFP database doesn't make it correct. For example, you can find a Chiquita banana that says 110 calories and another banana that someone put in with over 22,000 calories... and neither one may be right for your banana because they aren't based on the fruit's weight. Not all of the entries are right, and it is possible that the entries you are using are underestimating your calorie intake.

Good luck to you.