My mango tree is under attack

A mango tree which I have grown from a stone, has grown about 30cm (12in) high. However, white spots have appeared on the leaves. These are hard and flat and do not rub off easily. Some of the affected leaves are dying.

What you describe in your question are almost certainly scale insects. The white patches are protective, waxy layers exuded by the insects which settle down to live on the plant tissues beneath them.
One or two scales on a large plant do no harm but where the infestation is heavy on a relatively young seedling, they can be seriously damaging. Clearly, your mango tree is becoming stressed and the pest needs to be removed.
These creatures are difficult to eradicate because the waxy scale protects them from chemical sprays as well as from predators.
They can be prised off carefully by hand or you can scrape them off with a plastic plant label.
An alternative chemical treatment would be the systemic insecticide Provado Ultimate Bug Killer.
This is absorbed into the plant’s tissue where it will kill any insect that happens to feed on the sap.