Are the earnings of a father who prays only in front of people lawful or unlawful, and do his children fall under the noble Prophetic saying: "Any body that is nourished by unlawful earnings, the Fire is more deserving of it"?

Firstly: Abandoning prayer is one of the greatest sins; indeed, it is considered disbelief according to the more accurate of the two scholarly opinions. This carries implications both during his life and after his death, so it is necessary to continue inviting him [to righteousness] and advising him.

Secondly: The money he spends on you is not unlawful as long as he earns it through permissible means. The "ill-gotten gain" (al-suht) mentioned in the Hadith refers to money acquired through unlawful means.