1. protein shakes would be adeqaute, but for you, you don't need them right now; I'd focus on the training and diet.
2. Fat burning supplements are rubbish and unless people sit around stuffing their face with junk, then start stuffing their face with junk and consume pills, I.E.isolating the effects, it's virtually impossible to know if they actually do anything tangible, because as soon as you add exercise and / or diet changes into the mix, you've got weight loss factors, that other non-pill users could potentially use to lose weight, making the pills effects virtually impossible to ascertain.
Most supplements like that, including appetite suppressants and thermogenic serums, come with possible side effects including serious ones in some cases, I.E. Hydroxycut Hardcore killing people, so I'd avoid those, like most cats avoid water; if you catch drift.
3. If you're going to exercise, you might end up with a starvation mdoe, where the body assumes it's being starved and holds onto fat, so more calories would be wise.
1lb of added muscle burns an extra 45-50 calories per day, so losing it can cause more potential fat storage, so exercise and current caloric intake may possibly encourage weight stagnation or even a little gain, if muscle preserving nutrition, is not adequate enough to stave off potential exercise induced catabolism / atrophy.
4. Right now, I'd suggest around another 500-600 calories a day, so you're above the sedentary 1,800 female average and then you'll get more micronutrient intake as well, because whatever additional natural resources exercising will utilise, extra micronutrient intake should hopefully replace, so you're not potentially putting internal systems, particularly skeletal structures, into a regressive physical state, as Bones have many constituents and mediating nutrients affecting their structures, like Calcium, Vit K2, Vit D, Copper, Vit C, Phosphorous, Magnesium etc. More than probably any other internal structures.
I would reccomend if your carbs are bare minimum 20g per meal and more likely 30g per meal on average, increase from Fats and Protein, so if you eat 6 meals a day, you could do this with a 50/50 split, so from say 100 additional calories per meal, that's around 5.5g added Fats and 12-13g protein as approximate numbers.
The fats could easily be sourced from edible oils, but if you consume foods with multiple macros, like Peanuts, Soy and Soy products I.E. Edemame, Tofu, Nattokinase, Miso etc, Low Fat Cheese, Flax, Omega 3 Eggs, (Chickens fed some Flax in their diets), be aware that all those contain Carbs; the Omega Eggs have 1g, so don't worry about that and therefore you could slightly reduce any portions of predominantly Carb foods, like Veggies and Fruits, to account for this, unless you think your carbs may be currently too low in which case I'd keep Carbs as is, is you consume any of the types of aforementioned foods, or slighty increase current portions of predominantly carb based foods to top up carbs ot the sort of levels I suggested.
As you will be consuming more calories than usual, about 40% more based on current intake, you may find for a week or so, maybe a bit longer, you get some possible minor weight gain, as the body will be used to 1,500 calories a day and may possibly see an additonal 500-600 a day, as mostly excess calories, that can be converted to Fat, but if this happens, it should hopefully be minimal and with the body getting used to regular exercise and small amounts of muscle building, any such effect should be reversed, until you eventually, with any luck, surpass where you're at now and get leaner still.
Hopefully all this makes sense.
Good luck
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