Can a big bang happen again?

So if by Big Bang you mean the initial event, then no, there does not seem to be another Big Bang happening in our universe any time soon. Because of the dark energy domination, the expansion of the universe is accelerating (not slowing down, which could be the case if the universe were matter-dominated).

Is the heat death the end?

Yes. The heat death of the universe is the end state of a universe that’s ruled by accelerated expansion forever. Every gravitationally bound system — galaxies, clusters of galaxies — gets more and more isolated from one another.

What will happen to the universe after the heat death event?

Something like the air on one side of a room (that’s in thermal equilibrium) suddenly getting 1° warmer while the other gets 1° colder would literally be the least likely thing that’s ever happened. The universe suddenly “rebooting” after the heat death is… less likely than that. Multivac interventions notwithstanding.

What happens if you wait forever in the universe?

Physicist: If you wait forever, then you might see something happen. But the more practical answer is: no. The universe does a lot of stuff (for example, whatever you did today), but literally everything that ever happens increases entropy.

Does entropy ever reverse itself after heat death?

Yet another example of the scientific conspiracy at work! Long story short: yes, after the heat death there should still be occasional spontaneous reversals of entropy, but they’ll happen exactly as often as you might expect. If you break a glass, don’t hold your breath.

Does everything that happens in the universe increase entropy?

But the more practical answer is: no. The universe does a lot of stuff (for example, whatever you did today), but literally everything that ever happens increases entropy. In some sense, the increase of entropy is equivalent to the statement “whatever the most overwhelmingly likely thing is, that’s the thing that will happen”.