These are both really good questions and i am sure others have had the same thoughts. To begin with, if you are in treatment then you leave all of that up to professionals. Your dietician will know how many calories you eat and how much your body needs, you dont need to worry about any of that and your doctor and the staff will know your weight and know whether you are gaining or losing or maintaining and based from that your dietician changes your meal plan. Treatment is always recommended by me as i believe that for most of the time that is necessary. Sometimes its not actually the treatment that helps you recover but the fact that you have been in hospital, you hated it and realised you never want to go back there again so you choose to recover on your own - that works as well. But in recovery you need proper help and support and people who know what they are doing (which however isnt the case for all treatment centres). It can be comforting for some to not have to deal with the calories and the scale, to just leave it to someone else and to follow orders.
For me personally i found it comforting but also every anxiety filed and nerve wracking. I still calculated the calories on my meal plan and whenever i got a chance i would try to sneak a look at my weight or weighed myself if there was a scale. But that just caused anxiety and they were obsessions i had to break. Because you shouldnt get anxiety when you weigh yourself or feel bad for eating something with 200kcal instead of 100kcal. Its all energy and fuel which your body needs and will use.
If you are recovering on your own with no treatment then you do have to weigh yourself and count calories.... or atleast make a meal plan for yourself. That is what is recommened. I would say that you begin with making a meal plan with 5-6 meals and you aim to eat around 2000-2500 (depending on what stage of recovery you are at and how much you were eating before). While i was at Mando we used the Mando Meter (this type of scale) which then weighed our food so we were eating enough, but i would NOT weigh food at home. Instead try to think if you're going to have a bowl of yoghurt then fill the bowl, or take 1-2 handfuls of nuts or 3 crisp bread and enough butter to spread on the whole bread/crisp bread. And with dinners and lunches think 40% carbs,30%protein, 20% veggies, 10%sauce(or 50%carbs total) on the plate. So what if somedays you eat more or somedays you eat less, but if you follow your meal plan where it says what food to eat then whether you eat a little more one day or a little less the other day that is just how normal eating is anyway. HOWEVER if you feel that it can help, then you can begin with weighing the food for the first while until you begin seeing the portion sizes and then for your own sake try to step away from that and just use eye measurements.