1) PCOS, being a syndrome, is a bit hit-or-miss with regards to how it influences bodyweight (to be diagnosed with a syndrome, you basically just have to tick a certain number of symptoms out of a list of related symptoms, so each specific issue isn't necessarily experienced by everyone with the syndrome). But the fact that you're not heavy now indicates to me that PCOS probably won't be a very limiting factor for you. I once trained a woman with PCOS who was more than twice your weight at the same height as you, and she still managed to lose weight at a fairly normal rate when I trained her. In any case, at 54kg you probably don't need to lose weight. Recomp, maybe, but not lose.
2) In the context of 24 hours, I don't see that it really matters what ratio of fat vs carbs is burned up for energy during exercise. If you burn 500kcal worth of body fat, then that's 500kcal worth of body fat removed. If you burn 500kcal worth of glucose, then that's 500kcal worth of body fat that won't be accumulated. So I never bother with targeting an optimal heart rate for fat-burning during training, nor do I see much benefit in training on an empty stomach. Even if 500kcal taken out of the stored body fat for exercise were better than 500kcal taken out of the blood stream for exercise before it could be converted to fat, the absence of performance-oriented nutrition prior to training will reduce the quality of your workouts, and (as I've learned through experience) can cause all sorts of issues due to the extremely low blood sugar levels produced by fasted training. Notably, there's a correlation between PCOS and diabetes, so this should be especially important for you to pay attention to. Make sure you've eaten properly before training so that you can do your best while training.
3) I expect that your 800kcal/day is too low, but since you have a metabolic condition, it would be unreasonable to assume that your metabolic rate will live up to expectations. If you didn't have PCOS, I would suggest you consume closer to double you current calorie intake, possibly more. Since you do have PCOS, I really can't say.
4) I'm no good for recipes, sorry. But go for the important food groups: meat (any), dairy, fruit and vegetables. For the average person, anything else may be beneficial, but isn't direly important for good health or improving body composition. Since you have PCOS, you may have some special dietary requirements beyond this.
5) Again, depending on what signs/symptoms you have for PCOS, you may have specific meal-timing requirements for best health and functionality, but for body composition issues, it doesn't really matter whether you have your calories spread out across 6 small meals or 1 big meal, or anything in between. So, do whatever allows you to stick to a consistent plan without too much misery.
6) More exercise isn't always better, and this is especially true while aiming to lose bodyfat, due to recovery issues (the body recovers fastest when it's receiving more calories than it needs, and slowest when it's receiving less than it needs). But the most honest answer is: it depends. There are too many factors at play to say.