Restart button again

If your BMR is 1600, I'm guessing you're not overly heavy / do not have a lot to lose - so 2lb a week is almost certainly far too fast. Read other posts on here over the last few days and in the top posts of this category for far more info on what can happen if you eat too little, what's a sensible rate of loss etc.

MFP is designed for you to put accurate info about yourself and your activity into the site, select a sensible rate of loss and follow what's suggested. You're also supposed to track your exercise calories and eat those too, although many people find that exercise burn is over-estimated so they choose to eat 75% instead. That's what has worked for many many people on here, because it's tried and tested. If you're sitting all day and doing a walk 3x a week, I'd be inclined to select sedentary and then, separately, track your walks as exercise (but be realistic about how fast you're actually walking - a 30 minute walk at 3mph (my slow speed, due to a current foot injury) only gives me 98 extra calories).

You know from your original strategy what to do to maintain - knock 500 calories a day off that and you'll have the relevant figure for 1lb a week. Do that for a month, see how fast you're losing and adjust accordingly.

Your weight will fluctuate every day, so seeing an increase when you're "4 days in" isn't particularly surprising. Water, bowel movements, the weather, different levels of salt intake, exercising one day but not the next … these things all affect us. Put your weight into the app / use a weight tracker - and look at the general trend over a period of weeks.

The best plan I can suggest is to be consistent for a month (as you've done), get the stats from that and then adjust based on real results.

I'm 3rd-ing that opinion, as another who successfully lost 50 pounds, and kept it off.

Don't try to lose much more than half a percent of your body weight per week, unless you're severely obese and being monitored medically for nutritional deficiencies or health complications. It's too risky health-wise to lose fast, plus harder to stick with. The harder it is, the more frustrated we get when there aren't quick, dramatic results. Don't do it.

Half a percent, if you weighed 150 pounds, would be 0.75 pounds per week; at 200, 1 pound per week; and so forth. Slow and steady is the way to go, for success in addition to health.

Another way to look at it is to cut no more than 20-25% off your TDEE. If 1500 would give you 2 pounds a week (in theory) that implies your TDEE must be estimated around 2500 (assuming your settings are accurate). A 20-25% cut would have your goal at 1875-2000 calories. That's a lot of guesswork, though - treat that as an example of the arithmetic, not a directive about what you individually should do.)

Four days is not enough to tell anything at all, particularly if you've changed exercise or eating style (beyond just calories) at the same time. A month at least with the same routine, or a whole menstrual cycle if you have those, so you can compare body weight at the same relative point in at least 2 different cycles.

The calculators (and fitness trackers, MFP) are just telling you the average calorie needs for someone who filled in the boxes in the app the way you filled them in. Individuals differ. If you invest a month/cycle at minimum on a given eating/activity routine, you'll get personalized insight into your individual calorie needs, which is information very much worth having. That's true even if you gain a little over that month. (Trust me, with any of these number, if logging is remotely accurate and no major health crisis in play, you won't gain 15 pounds in 30 days, no matter how it looks after 4 days.)

Invest the time. Stop starting then failing than re-starting. Patient persistence is what succeeds.

Best wishes!