Is it necessary for everything to have a cause? Can events occur without any reason or cause?

It depends on what you call “A reason or a cause.”

For example, if an airplane falls from the sky and only one person survives, albeit disfigured.

Some people might say that it was a Miracle and happened for a reason… :) The survivor may become a religious zealot (for example) and attribute his survival to God, the Almighty.

Of course, that is not a reason. It doesn’t make sense to kill everyone and maim and disfigure the person just to make yet another religious person. By the way, the person might already have been converted...:)

So, reason and cause are words used differently by different people.

If, on the other hand, you are speaking of a “physical reason, " something that happens because some Law of Nature demands it to happen, then one can say that the airplane fell because it lost its engines and velocity. Without velocity, aerodynamics laws (laminar flow on the top and bottom of the wings) stopped providing lift. Without lift, the other Law of Nature (Law of Gravitation) forced the free fall and acceleration.

Eventually, the ground stopped the flight (due to the Exchange Interaction between the electrons of the airplane and the ground).

So, everything that happened, even at the microscopic level, had a reason or was governed by a law.