You're forgetting something VERY important here. As an example, consider this, if someone starts to workout their arms using 20lbs dumbbells (with no previous experience), they will eventually get stronger and the 20lbs will be easier than they were before right? So, now what if that person kept lifting 20lbs even after they got stronger? Do you think they're going to keep getting stronger? If that was the case, why would the gym need a bunch of dumbbells ranging from 10 to 200lbs, if you could just not change things up and progress? Do you get what I'm saying here?
You must understand that the human body is incredible at adapting. If, for example, you burn X amount of calories by walking 5 miles per day, your body will adapt. It will make its energy pathways more efficient and you will burn less than the X amount of calories that you used to burn, your body loves trying to save energy (hence why it stores extra as fat or glycogen). Same goes for any other physical activity you do, you MUST progress, either walk faster, longer, or more often.
Now that we got the most fundamental point down, there's still a lot of reason that can cause your situation, and I will outline the most common/reasonable explanations. Also I have no idea why you're adding 600 calories to your RMR, you should be subtracting it. If you're not losing weight with the amount of calories you're eating, its very simple...just reduce the calories.
You say you want to lose weight in the healthiest way possible but you also say you don't lift weights. This is almost a contradiction. If you don't lift weights, when you do actually lose the weight, you will undoubtedly lose muscle as well (even if the majority of the weight was fat). If you lose muscle, you lower your metabolic rate. If you lower your metabolic rate, you now need to consume even less calories than before in order to lose weight. So if you needed 2000 (your RMR - 500 for example) calories a day to lose weight, and didn't weight train, and then you lost 5 lbs (3 lbs fat 2 lbs muscle). And after this, you STILL consumed the same amount of calories, you are now going over your maintenance calorie levels since you dropped your RMR by losing muscle, and hence you will actually gain weight! And since you don't weight train, you definitely didn't gain muscle, and now its gonna be even harder to lose this weight since your RMR is dropped! Do you see the contradiction now?
Nevertheless, you can still lose weight in a healthy way without weight training, it will just be a lot harder and not the "healthiest" way possible.
Your apetite increasing in the last few months can be explained by leptin.You eat below maintenance calories over a period of days or weeks. Your fat cells shrink as you diet, not eat, etc., and fat cells release less leptin.
Your brain senses that leptin levels are low, and that you are no longer "fueled up." The hypothalamus senses the decrease in leptin levels, lowering metabolic rate and decreasing energy expenditure. It also sends a "hungry" signal, increasing appetite and encouraging you to eat. Leptin action isn't confined to just the hypothalamus. There are leptin receptors all over the body. This allows leptin to precisely coordinate appetite, metabolism, and energy expenditure.This is nature at its finest. Your body is programmed to survive. To combat this, it's actually not a bad idea to have "refeed" days. This would be a day (every two weeks or something) where you eat above your maintenance level calories in order to shock your body, so it doesn't adapt to lower calories and stall your progress.
Moreover, the sources of your calories matter. The less protein you eat, the more you risk muscle loss and hence lowering your metabolic rate which will make losing weight harder and even cause weight gain. The types of carbs you eat also matter. For example, if the majority of your carb sources are high-glycemic foods such as white rice, white bread, cereal, pasta, fries...etc, then you will over time build up insulin and leptin resistance (remember leptin is key). Insulin resistance will make it so that you can't utilize future carbs effectively for fuel and make you store them as fat easier. While leptin resistance will increase your apetite without you actually needing more calories.
Now, sorry I went on a huge squeal about this stuff, I just saw your real 3 questions, but luckily they're easy to answer.
Caloric Intake per day?
Obviously, every person is unique and will respond differently to different situations. You say your RMR is around 1960 from online calculators and this is a good place to start but you have to remember to experiment. There is nothing linear in the world of fitness and nutrition. If you're eating 1900 calories a day per weeks and not losing any weight, obviously the only sensible thing to do is reduce the calories, personally I would reduce by around 200. Also note that you added 600 to your RMR. What I personally do is reduce 600 not add it so that's interesting. Im currently prepping for a competition and have been steadily dropping a pound each week for 5 weeks.
How should you divide per meal?
This is highly individual and depends on your goals. However, the best time to consume carbohydrates are period of high insulin sensitivity. This would be right in the morning when you wake up, and right before and after your workouts. Remember the main function of carbs is energy, so ideally you want to minimize their intake when you don't actually need them or it will be harder to burn fat. On the other hand, you don't wanna eliminate them completely because you will lose muscle easier. So for example, morning meal: high protein med carbs low fat, snack: high protein low-med fat, pre-workout: high protein med carb, post workout - high protein med carb, lunch/dinner and rest of the snacks- high protein med-high fat.
Basically, just eat carbs around the workout and the morning. Eat fats when you dont eat carbs for energy. Eat protein ALL the time.
Any other suggestions to stay healthy?
Lift weights. I can't stress this enough. When you first lift weights, you will gain muscle (healthy weight) increase your metabolism and so many more hormonal benefits its actually crazy not to workout. Also, do some research around the internet (from cited articles) regarding your goals. There are lots of great sites for this, bodybuilding.com, simplyshredded.com etc...