How it can be known that ignorance won't return/re-arise or why it won't return/re-arise if there is no consciousness at the time.
“Bhikkhus, there are these five higher fetters. What five? Lust for form, lust for the formless, conceit, restlessness, ignorance. These are the five higher fetters. The Noble Eightfold Path is to be developed for direct knowledge of these five higher fetters, for the full understanding of them, for their utter destruction, for their abandoning.
“What Noble Eightfold Path? Here, bhikkhus, a bhikkhu develops right view … right concentration, which has as its final goal the removal of lust, the removal of hatred, the removal of delusion … which has the Deathless as its ground, the Deathless as its destination, the Deathless as its final goal … which slants, slopes, and inclines towards Nibbāna. This Noble Eightfold Path is to be developed for direct knowledge of these five higher fetters, for the full understanding of them, for their utter destruction, for their abandoning.”
So ignorance won’t arise anymore because an arahant has cut off all 10 fetters. Ignorance is one of those fetters. An arahant have direct knowledge of these fetters and he knows their destruction and he also knows if the fetters are abandoned or not.
It seems to me that consciousness is required for knowledge, so when an arahant dies how can there be knowledge and thus certainty that ignorance won't reform/re-arise after death?
When an arahant dies he is free of the 10 fetters including ignorance and he also know the four noble truths so he will not be reborn. At the moment of his death, there was no ignorance so all things in the dependent origin that comes after ignorance will not arise because ignorance is not present at the moment of death.
Is it through direct knowledge of the entire future that occurs before death?
An arahant usually knows that birth is ended. It is usually mentioned in the suttas.
Is it known through abhijñā i.e "direct knowledge", of the entire future, before the arahant dies?
There was one sutta where a guy asked an arahant if he has psychic powers but the arahant replied no. I can’t find this sutta so can anyone tell me. So the abhijna or the six higher knowledge aren’t required to be an arahant except the last one which is the ending of mental fermentation. An arahant can develop psychic powers after becoming an arahant but they probably don’t have any desire to achieve those powers.
"With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, the monk directs and inclines it to the knowledge of the ending of the mental fermentations. He discerns, as it has come to be, that 'This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress... These are mental fermentations... This is the origination of fermentations... This is the cessation of fermentations... This is the way leading to the cessation of fermentations.' His heart, thus knowing, thus seeing, is released from the fermentation of sensuality, the fermentation of becoming, the fermentation of ignorance. With release, there is the knowledge, 'Released.' He discerns that 'Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world.' This, too, is how striving is fruitful, how exertion is fruitful.
So as you can see, an arahant knows that he is released and that there will be no further birth.
Doesn't truly knowing something like that require omniscience?
No, only the Buddha was omniscience. An arahant would know that there will be no further birth because
1) The Buddha told them that attaining arahantship will end rebirth
2) When he is released there is the knowledge “release”
3) He knows there is no next life by looking into the future with psychic powers.
I think 1 and 2 are the most possible way to know that he will not be reborn because not all arahants have psychic powers. It’s not even needed to look into the future because arahant knows that there is no further birth.
How does one know that the abhiññā is true? It seems to me that omniscience is required.
If you are literally flying then you would know there you are flying. If you can travel to other realms then you would know it. Omniscience is not required. You don’t need omniscience to know that your memories are real or not. If you try to remember what happened just an hour ago then you know that memory is true. In the same way, when you recollect your past lives you know that it’s true. Abhinna are as real as moving your hands or legs. So you will know if you have abinna or not.