If you don't have a copy of your parents' ID card, are you eligible to apply for a visa? If so, can it be successful?

Need more information. Which country and what kind of application?

Suppose your parents are divorced, so although there are several places to fill in his name on the application form, you don't need to identify him because he won't immigrate with you.

Anyone can apply. Foreign consulates need to see China passports, not ID cards. Passport must be available, if not, you should apply immediately. And the visa needs to be posted on the passport page. They can't get through without passports.