Well what I can say is, is that you're definitely getting some spinal lordosis in the lower back on the first picture, which is basically inward curvature of the lumbar and sacral vertebrae.
So I would suggest trying to walk by planting the ball of your foot on the floor and then landing the heel. Avoid things like heel strike, as you'll potentially get shin splints and that can affect runners who don't use proper technique.
I would also at all costs avoid wearing heels, as I find them hideous to look at anyway from the make perspective, but they're extremely bad regarding things like blisters, tendonitis, calf problems, deformation of the toes and may even cause damage to the bones in the ankle and shin and if you ever hear anyone tell you "you have to suffer pain to look good" or "to walk through the pain", then they're out of their tree and inflicting actual pain on the body repeatedly, is extremely unhealthy and a very poor way of regarding yourself and right now it's about trying to walk in a normal fashion, so as to avoid the anterior tilt and lordosis and correcting the issues you have been living with up to now

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You could try the technique models use where you balance books on your head and try to stop them falling off and see how that goes.
As for the gym, I understand your concerns and I personally think you'd be fine because the vast majority of people in places like that, are just there for themselves, not so they can treat other people like dirt, or judge them for what they do, but if you really feel right now like you cannot handle that environment, then I'm not going to coerce or persuade you to do anything like that, because I don't want to put you in a situation where you get emotional concerns after a while and ditch exercise, which is what you said might happen, so I suggest you train at home and do something that is not going to take a long time and will be easy to manage.
This is what I think you could do and please do ask for clarification if there is anything you don't quite understand

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Squats, 12 sets 10 reps
Lunges, 12 sets 10 reps
Good mornings, 12 sets 10 reps
Vertical flyes, 12 sets 10 reps
Bent over Rows, 12 sets 10 reps
Shrugs, 12 sets 10 reps
Planks 30-45 seconds.
You can do this as a weighted system by improvising and normally I just suggest this for home workouts as a body weight routine, but as you say you want at some point to go to the gym, then I would like your muscles to be given some acclimatisation to load bearing exercises, so when you go to the gym eventually your body will be able to tolerate that and you might be able to start at a slightly more intense level than the average novice.
So what you will need for this are 4 books to hold. You need 2 small ones of equal size, around A5 size and 2 larger ones closer to A4 size, but don't use any that are really chunky like a bible, or a dictionary, or one with loads of pages like war and peace

, just try to use larger ones with maybe around 100 or so pages if you can, but if this load bearing strategy is a bit uneasy, we can tinker with it, I:E: using a couple of filled up water bottles for example, or even using a pair of shoes, but I'm hoping the books strategy will be okay for you.
The workout will be done 3x a week every other day.
As for the diet, there are plenty of things you can use to base a diet on and normally I have a system that I give to many people, but as you need time to develop consistency regarding a regular eating frequency, the emotional / mental demand of eating the sort of calories it would provide might be a little too much just now, so I'll give you something that has the frequency you need but doesn't allow you to feel like you're going overboard on calories and then in the near future you would be ready to eat more, so that you'll be eating closer to the sort of daily calories that will be normal and of more benefit to you, but right now I don't want to push this aspect of your wellness too much, in case it harms your mentality toward regular eating

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There are many things you can use to base snacks on such as bread, sandwiches, ham, beef, turkey, pork and chicken from a packet, boiled eggs, nuts, peanuts, low fat cheese, low sugar yoghurts, vegetables including pineapple, celery sticks and raw carrot, fruits including tomato and cucumber flax seeds and oat granolas.
I often espouse microwaved options too, but they may be a bit calorie rich and being heated up, they wouldn't really keep until later, whereas some oat granolas can be more calorific than others, but any leftover granola can be saved until later in the day, so the alternative to microwaved baked beans or soups is to use tinned stuff cooked on a stove, so you have more say over the quantity and limit wastage.
As for the main options, you can use those snack options, but you could have things like scrambled eggs, toast, cereal and grapefruit with breakfast as examples of other things to have, but in relation to grapefruit and its juice, if you're taking any medications right now, check if it is contraindicated with them first, as grapefruit and associated products, can interfere with some medicines and in one persons testimony on this site, she said a relative of hers had consumed grapefruit content in her diet whilst on medication and the reaction caused her sister to pass away.
I'm not trying to scare you regarding grapefruit, as it's a very good source of things like vit c, a and calcium, but obviously I'm just trying best to look out for you.
Also if you've had any reactions regarding eczema, then be careful of nuts and peanuts, as peanuts have in the past been linked to eczema outbreaks as have seeds, but otherwise if you haven't then don't worry and consider nut, peanut and seed options in your diet if you wish.
In terms of main options for lunch and dinner, the snack options would work as a basis, but so would other things like beans, other than baked of course, rice, mushrooms, min corn cobs, if you wanted to make a stir fry, chicken breast, lamb and pork chops and soy products like soybeans, miso, tempeh, tofu, nattokinase and edemame and also a more broad spectrum of vegetable options and along with beans, other legume options like peas and lentils, plus some fruits are good for cooking with or eating in mains, like tomato, cucumber, aubergine, (eggplant), marrow, avocado and chillies.
As I say if you need any clarification on anything I've said, please feel free. I want you to know that myself and the community are on your side 100% and we want you to find the happiness and confidence and enjoyment from life you deserve and I just wanted to send you a BIG HUG, just as an act of kindness and I want to let you know that like all members, if you ever have any worries or concerns regarding other site members or things going on in your life, send me a PM anytime and let me know what's up, because I will keep what you tell me in the strictest confidence at all times

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It's been really good to get to know you and I'm sorry you've had to deal in the past with a few unwanted comments and some personal issues like depression, because I certainly don't think you deserve anything but a great life and a lot of happiness and I personally want to help you find more of the happiness I believe you're worth, because you shouldn't have to have such a hard fight with your emotions and confidence and self esteem in the way(s), I imagine you have been doing and I want you to discover more of the beautiful person I think that exists in your head and heart and be able to have more control over your life and feelings, so whatever myself and the community can do, for as long as you want myself / us to, we will be here for you okay

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For now, chin up, be strong and anything else you need just ask, or if you need to talk about personal stuff message me and just say whatever you need to say however you need to say it.
THANKS for getting back in touch and please do keep in touch with us and let us know how you're progressing, because I for one would really like to know how you're doing and unless you don't want us to be anymore, we won't stop being here for you okay, but remember that you ARE worth it and you DO deserve to be happy

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