Eternity is not a long long time, it's the absence of time. Temporary is the opposite of eternal, it means temporal or existing for a time only. In this temporal world everything has a beginning, a middle and an end. The spiritual world is eternal. No one is born, no-one dies.
Physical re-birth would seem to be a fact. Re-incarnation means to make flesh again. Most people only relate it to being re-born in a body after death, but in fact from the moment of conception until the moment of death our body is constantly being made flesh again or transforming - this is metabolism. We are constantly re-incarnating in this very lifetime, and the final stage in this process is called death.
Enlightenment can't be measured in time, its an achievement. If we don't take the necessary steps to achieve it, we won't reach it no matter how long we wait. It's not just a question of ordering it and then enquiring about the delivery time. It can happen in one moment or take many lifetimes.
In Bhagavad Gita it says that any spiritual progress we make is never lost. Even if we are unsuccessful in achieving the goal this lifetime, we will start again from the point we have reached in a future birth. Enlightenment, heaven and hell are states of consciousness, not geographical locations. They transcend space and time. They exist in a different dimension of reality.