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I don't know about the Italy situation.
But the age limit on the UK e-gates is now 12 years old, provided supervised by an adult, who doesn't need to be the parent.
A letter isn't strictly required for the UK either, but it may help, and it can result in a telephone call to the parents or legal guardian. It doesn't need legalisation. The Border Force have several methods to verify names against telephone numbers, passports against relationships.