Final answer:
The sentence 'No one can ever really know their own fate.' is grammatically incorrect because it uses a plural pronoun 'their' for the singular antecedent 'no one'. The correct pronoun should be 'his or her' in formal English.
Step-by-step explanation:
The sentence which is grammatically incorrect is C) No one can ever really know their own fate. The issue here is the use of the plural pronoun 'their' to refer back to the singular antecedent 'no one'. In standard formal English, each singular pronoun should have a singular reference, so the correct form should be 'his or her' instead of 'their', unless the context allows for a gender-neutral singular 'they', which has become more accepted in informal usage.
For the other options, A) is correct because 'everyone' is a singular indefinite pronoun and is correctly referred to by 'his or her'. B) and D) are both correct because 'all people' and 'the whole family' are plural and correctly take the pronoun 'their' and the verb 'is' respectively.