Is there a specific age for an animal slaughtered for daily consumption and eating, and how accurate is the saying that the appropriate age is two years and less than that is not permissible?

There is no specific age requirement for slaughtering livestock for consumption. It is permissible to eat the meat of a lamb that is one day old or even younger, as the default ruling is permissibility. Whoever claims prohibition must provide evidence. The Prophet, peace and blessings be upon him, ate from an "anaq," which is the female offspring of goats that has not yet completed one year of age. A fetus born alive from its mother's womb becomes permissible to eat after ritual slaughter (tadhkiyah). Any stipulation of a specific age for consumption is an innovation in religion, as Allah Almighty says: "And do not say about what your tongues falsely describe, 'This is lawful and this is unlawful,' to invent a lie against Allah. Indeed, those who invent a lie against Allah will not succeed." (An-Nahl/116). However, a specific age is required for the animal if it is intended for sacrifice (udhiyah).