Well if we're going to express gratitude... I'm really hot today 
Current blog working title: Hot Snails
Asos also has the Vit C 23% in stock, Lego.
In terms of diet, it's complex. Cutting back dairy is useful for some (insulin resistance and/or hormonal issues) but not for everyone. In general basically similar to what you're putting on your face:
Antioxidants- all the vitamins, A,B,C,D,E, etc. basically eat loads of varied fruit & veg (the more colourful and varied the better), complex carbs, etc. EV Olive Oil is loaded with antioxidants, I'm personally not all that convinced by coconut oil.
Anti-inflammatory foods- Nuts are a great source of zinc (especially almonds). Also means avoiding inflammation-inducing foods like refined sugar, alcohol, etc. which can include gluten or dairy if you are sensitive to that or have difficulty digesting it fully.
Omega 3- preferred sources are oily fish like mackerel, sardines, salmon, etc. but it's also in things like chia seeds, flax seed, sea vegetables, etc.
Probiotics- fermented foods, yoghurt, kefir, etc.
Hydration- just beneficial to general health to drink enough.
There's probably more but in a nutshell, a varied diet with a lot of fruit&veg, complex carbs, (cultured) dairy, nuts, lean protein, etc. Moderation with sugar and alcohol. Be careful with salt and if possible avoid processed foods.
I'm actually having first world induced guilt around avocados, I've always been quite smug about how wonderful it is for the environment that I don't eat meat but apparently, the carbon footprint on avocados is just as bad or worse than meat 
I honestly don't know if you can eat your way to healthy skin, the opposite is certainly true but then it's often the case that there's an allergy or intolerance at play that causes bodily inflammation that's also expressed in the skin.
Ehm I just started with running at 5k back when I still ran, Dulci, moved it up to 10k 5x a week quite quickly (at a reasonable pace) but I'm weird with exercise. Can do long distance very easily but I injure easily due to overproducing a hormone usually only seen in pregnant women that keeps the body extra flexible in anticipation to cb, I cycle now instead. I did recently start jump roping (sp?) 3x a week, 20 mins total, which I find brilliant. I've always wanted to integrate HIIT workouts but the whole stopping and starting thing just annoyed me, this works brilliantly as it's sort of the natural rhythm anyway, I don't need to go to a gym specifically for it and can travel with it easily.
Well, yes apols for not getting back to you sooner and using you as an example. Going by your pictures I'm still convinced you're not bone dry and more likely in the normal-combo range with dehydration. I was wondering if perhaps you've had a lot of sun damage in the past around the nose/cheek area. I have a bit of this from childhood (never burned except on the nose) and subsequently have the enlarged pores only in that area.
I know you were asking about specific products so I'd suggest the following:
La Roche Posay Toleriane Dermo Cleanser in the AM and as second cleanse in the PM if you wear heavy makeup otherwise as single cleanser in the PM should work fine for now. If you're truly dry you're probably better off simply splashing your face in the AM.
Moisturiser, if indeed you are truly dry, try LRP Toleriane Riche, otherwise the Eucerin UltraSenstive for normal to dry skin.
SPF- General starting point rec here is LRP Anthelios XL Fluide SPF50+
I suspect dehydration with you so I'd look into something like Hylamide SubQ Anti-Ageing Serum or The Ordinary Buffet. I'm not familiar with moisture bomb but if that's like an oil-free gel-like hydrating cream that could work in the interim too.
Introduce things gradually, yada yada, and once you're on your way we can discuss next steps.