Will Hell be for eternity for unbelievers?

Will time still exist in heaven? In Revelation, it talks about trees bearing fruit every month which seems to suggest time still exists. Can humans even exist outside of time like God does? Second, is hell eternal or will it be a punishment for a set time (1000 years) and then completely destroyed?

Regarding time, Creation will also exist in a place of time and space, since this is in keeping with our nature. Only God is omnipresent and without a beginning. Timekeeping in the New Eternal Order will be done in months only, not in years. So we will know a pattern of life (i.e., twelve repeating months), but we will not know a counting of years since there is no end.

Finally, Hell is not the eternal abode of the unbelieving. Rather, the Lake of Fire is their eternal home, and it will last for eternity, as Jesus says:

Matt. 25:41 “Then He will also say to those on His left, ‘Depart from Me, accursed ones, into the eternal fire which has been prepared for the devil and his angels;
Matt. 25:42 for I was hungry, and you gave Me nothing to eat; I was thirsty, and you gave Me nothing to drink;
Matt. 25:43 I was a stranger, and you did not invite Me in; naked, and you did not clothe Me; sick, and in prison, and you did not visit Me.’
Matt. 25:44 “Then they themselves also will answer, ‘Lord, when did we see You hungry, or thirsty, or a stranger, or naked, or sick, or in prison, and did not take care of You?’
Matt. 25:45 “Then He will answer them, ‘Truly I say to you, to the extent that you did not do it to one of the least of these, you did not do it to Me.’
Matt. 25:46 “These will go away into eternal punishment, but the righteous into eternal life.”

Notice, Jesus compares eternal punishment to eternal life. Just as we live forever in glory, the unbeliever lives forever in punishment. You can read more about the reasons for eternal punishment in this related article "Did Jesus have to stay in hell longer?"