Since you say you are new to physics first of all let's state what energy is. It is defined as the physical quantity which measures the quantity of work a body can do. Work is the product of a force and a displacement along its direction. It can be thought as the "effort" you (in general the force) have to do to move an objet by pulling it.
In this case the type of energy the water gets when falling is kinetic energy, that is the energy that a body has due its motion. From motion comes a possibility to do work and this happens when the body slows down. As an example you can consider a bullet moving towards a can; when the bullet hits the can it slows down and the can starts to move, what happens is that the bullet decreases his velocity and thus loses kinetic energy while it does work on the can. Doing work on an object entails transferring energy to it.
As you correctly said energy cannot be created, so where does the kinetic energy of the water come from? There must be a force doing work on it and so transferring energy to it. This force is the gravitational force, i.e. the force that "pulls" all the objects towards the ground.
To see this as an energy transfer we can consider an energy that accounts for the possibility the gravitational force has to do work on an object. An object is said to have gravitational potential energy if the gravitational force can do work on it and depends on the mass of the object and height. So what happens during the fall of the water is the transformation of gravitational potential energy in kinetic energy.
To put this into formulas the kinetic energy is given by
$$E_k=\frac{1}{2}mv^2$$
and the gravitational potential energy is given by
$$E_g=mgh$$
where m is the mass of the object (here the water), v is his velocity, h is hi height and g is the acceleration due to gravitational force.
While the water falls v increases and h decreases, so the kinetic energy increases and the gravitational potential energy decreases, and this happens in a way that the total energy is always the same. (If there is no friction).
On the water-splash, here's a video that I think explains what happened. https://www.youtube.com/watch?v=2UHS883_P60 (the 3 balls, not the double bounce on the trampoline).
The Newton law of conservation of energy says that energy is concerved, so a share of the energy of the drop transfers to the energy of the splash.
Figure you drop it from 1/2 meter and the mass is 0.2 KG (about 7 OZ). Do a little math and 1/2 * 9.8 * .2 = .98 Joules, or about 1 joule of energy.
How high a splash can 1 joule make in still water, well, it depends. The energy is converted into 3 different types of energy, wave energy, which is likely the biggest share, splash energy (#2), which depends on a few factors like the shape of the object, depth of the water, if there are already waves present, etc, and the 3rd and likely lowest of the 3, heat energy. Here's where the YouTube video comes in. If it splashes just right, you can get much more velocity out than you put in, into a much smaller mass.
There's no good calculation that I know of to give you maximum height a water drop can reach in this scenario. It depends on how well the energy transfers into a drop and what size drop.
As you know from experience, this kind of splash-back is rare, but dropping from a lower height or dropping one at a time vs 2 at the same time should reduce the likelihood of a high splash - that's probobly super obvious.
A curious and loosely related field of study is wave size from large meteor impacts or landslides into the ocean. A rather fun one to read about is the Canary Islands waring, that one research team made and others think they exaggerated, but it found it's way onto television and there were warnings that a Canary Islands landslide could create 50 foot waves across the entire eastern seaboard". Probably not accurate, I think, but the warning made some impressions all the same. More on that here: http://news.bbc.co.uk/2/hi/science/nature/3963563.stm
Best Answer
It wont be unboundedly fast e.g. due to the viscosity of the water.
In addition, I'd like to point out that you won't have the cylinder of water. Water will accelerate with gravity as it falls. The density of water is constant. The total flow of the water at different height is constant as well. So the area of the water's cross-section will decline.
For thin stream of water from a kitchen tap, surface tension force is enough to keep the water flowing in one stream, but the thickness of the scream decreases, take a look here.
However, as you increase the initial radius of your stream, the water mass (~R^2) grows while the pressure gradient created by surface tension forces (~1/R) declines. That's why the cylinder will pretty quickly separates into multiple streams, and eventually into droplets..