Hi, yes , SW does work -If you follow the plan , I have lost weight many times following it - just put it back on each time I start eating rubbish and having binges on chocolate etc
It's all about filling up on the speed/free foods and if you do that it naturally reduces your calorie intake - and there is also the ''in moderation'' side of things - like yes. pasta for example is free but if you ate like 10 big bowls of it a day then no you wouldn't lose weight (or very slowly anyway) - and adding a third of ''speed'' foods to your meals will fill you up for a lot fewer calories.
It is a very good plan if you follow it properly.....
1200 calories doesn't seem a lot and is probably not enough - the calories you need depends on your BMR and activity levels - and everyone is different - dependant on weight/activity and when you know how many calories your body needs to live and do the things you do daily - you just take of 500 cals per day so you're in a calorie deficit, and that should lose you a healthy 1-2 lb a week
At the end of the day it's about a healthy eating lifestyle change, and all the ''junk'' foods should really be ignored or eaten as a treat or in moderation - a healthy balance is what's needed