Битые ссылки можно самостоятельно починить по смыслу же. Поменяли структуру сайта МИДа, но информация там есть.
https://mfa.gov.cy/application-process-and-requirements.html

Правда, про перевод документов и там ничего нет.
Зато есть
Applications concerning minors must be submitted together with a letter signed by both parents or legal guardians, authorizing the minor to apply for a visa to enter the Republic of Cyprus. Proof of the relationship between the minor and the authorizing person(s) is also required (documents accepted: copy of ID or passport of each parent, accompanied by a copy of minor's birth certificate stating the parents' names; death certificate, where applicable, and, in the case of sole custody, a copy of a judicial document attesting that).