How to avoid the blackening fruits once they are cut?

I am aware that this is quite late.

Blackening and browning of fruit is caused by the oxidation of polyphenolic compounds in the fruit by a class of enzymes known as, perhaps unsurprisingly, polyphenolic oxidases (PPOs). PPOs are found inside the cells of the fruit you are eating and are released when you rupture the cell wall and membrane when the fruit is cut. Exposure to oxygen activates the biochemical pathway, resulting in the browning you see.

There is one simple way to prevent function of PPOs is to soak the fruit in a salt solution. Interestingly, a low (acidic) pH enhances this effect. The full version of the linked article goes on to explain that a 0.1 mol/l solution is enough to inhibit browning in a blinded observational test. Sodium Chloride, the common table salt, has a molar mass of 58.44 g/mol., so for a 0.1 mol/l solution you need 5.844 grams (0.206 oz, or about 1 teaspoon) of salt in a litre (2.11 pints) of water. Soaking for 3-5 min is plenty and will not cause substantial salt uptake on the fruit.

This is highly effective at inhibiting browning - I use it all the time on cut fruit for my children, and it will last all day with ease.

Browning does not affect nutritional value particularly. The action of the PPOs is limited to the cut surfaces, and most fruit contain about 0.2-0.3% by weight, so there is plenty there beyond the cut surfaces. Polyphenols are generally classed as anti-oxidants, so they are probably of some nutritional benefit, but if you eat a healthy balanced diet with fresh fruit and vegetables you should be getting plenty of antioxidants anyway. Some polyphenolics are classified as tannins - the dry/astringent components in some wines and tea for instance. These can make food unpalatable, but are not harmful.