I'd say best policy re shaving would be whenever she is self conscious of body hair that she can shave. What difference is there between say 13 and 14 in the "dangers" of shaving, if that's what you're concerned about.
I think letting her buy her school uniform herself is a strange thing to do at Any she quite frankly! Not a passage of rites I don't think!
Re the dress not fitting, did you not try the next size up?
I'd recommend a shopping day, try lots of different styles of clothes and sizes from different shops. Teach her the reality that a size 10 in Zara might be a size 8 in new look and not to give a damn about what size she is, but to buy the article that fits best. I range from a 12 to 16 in jeans for example!
Re weight gain, if she loses weight (and needs to) if she then gives up of course the weight will go back on. You need to find a sustainable healthy eating diet and exercise programme. Dance lessons or Zumba on YouTube? Doing 10k steps, couch 2 5k all free!
Re crop tops, are you talking about training bras or (to quote my grandmother m) "midriff bearing tops" to wear with leggings etc. If the former, get the poor child a bra, changing for PE is mortifying. If the latter yeah it's awful (for most ages) but it's fashion. All I'd suggest is if she really is big and self conscious a crop top probably isn't for her (though I do believe in wear what makes you happy, but if she's already self conscious that won't help) and encourage her to look at the other lovely fashions at the mo; Hugh waisted trousers/jeans/skirts, midi dresses etc!
Re makeup, if she's got bad eczema she and you need to be really careful with what products she puts on her face. I speak from first hand experience. Don't just let her play with cheap makeup without researching the ingredients. Perhaps she's self conscious of the eczema hence the interest in make up, that's understandable. But teach her to apply natural looking makeup (no orange faces and ridiculous eyebrows) and importantly teach her to remove it properly at night and to care for her skin properly including moisturising.
Hope that helps