Why is the Death Star shaped like a sphere?

Everything with mass has gravity between it and each other thing with mass. There's gravity between you and your computer, but it's too small to have any noticeable effect.

For the effect to be noticeable, at least one of the bodies needs to be big, and not too far away. For example, the earth is big enough to keep us on it unless you have a big, powerful rocket. The moon is big enough and not so far away that it causes tides. The sun is big enough to keep the earth in orbit.

Gravity can be calculated as a tiny constant multipled by the mass of one object multiplied by the mass of the second object divided by the square of their distance. F = G * m1 * m2 / r^2.

So the Death Star: "It's colossal, the size of a class-four moon". But how big exactly? Wookiepeedia says:

The first Death Star was 160 kilometers in diameter, while the second Death Star was 900 kilometers in diameter.

A recent Reddit post puts this into context:

The Death Star is not nearly as massive as you seem to think it is. In another recent Star Wars thread, I calculated a rough estimate of 6.777x10^17 kg, which is roughly 1 / 108,395 the mass of the Moon or 1 / 19,389 the mass of Pluto.

That said, it still has some effect on other astronomical bodies, but not a significant one. To give you some idea, given the mass I calculated above and a radius of 80km, it would have a "surface gravity" of 0.7067 cm/s^2 which is 1 / 1388 the gravity of Earth. If you weighed 180lbs on Earth and were to "stand" on the hull of the Death Star, you would exert a force of about 2oz.

Others point out that the ship had artificial gravity generators, it's mostly all aligned up-down decks, so the ship's own natural gravity wouldn't make any noticeable difference. Wookieepedia again:

The Death Star's interior followed two orientations. Those areas closest to the surface were built with concentric decks with gravity oriented towards the Death Star's core. Past this shell of surface "sprawls", the Death Star's interior had stacked decks with gravity pointing toward the station's southern pole.

Also from Reddit:

The Death Star uses massive inertial compensators in order to allow it's massive bulk to be moved about easily. Since inertial mass is equivalent to gravitational mass, the Death Star exerts a much smaller gravitational field than it otherwise might. It's still very heavy even with it's inertial compensators up, it just won't [knock] planets out of orbit.

Finally, for something travelling in the vacuum of space, shape doesn't matter as there's no wind resistance. Other ships need to land on planets and fly in their atmospheres, but not the Death Star which was constructed in space.

In the first movie, Luke mistakes the Death Star for a small moon the first time he sees it, as shown in this clip. There isn't any further implication that the Death Star was MEANT to resemble a moon.

In the novelization, however, there was a passage about the Death Star being covered in lights that could be turned on and off to mimic the phases of the moon. That's really kind of ridiculous, though, since when it comes close to a sun, it would show the phases of a moon naturally.

If the Death Star was sufficiently massive to generate a gravity field, as seems likely, the artificial gravity system would probably have been designed to counteract it. The Earth's moon has gravity one sixth that of the Earth. A "small moon" would have less.

Is there any mention in the Star Wars movies about why a sphere-shape was chosen?

The triangle, letter X and square had already been used. Only the blueprints were smuggled out of the Empire, but many Bothans died to smuggle those blueprints. I fear the answer died with them.

It would seem that the shape is unreasonably hard to make.

Agreed. This is why they had to double their efforts to finish the Death Star before the Emperor arrives in Episode 3.

Molding perfectly all the outer plates does seem to require every plate to be unique.

You can make a perfect sphere out of small hexagon shaped panels that are all of the same size. You would only need uniquely shaped panels if it was not spherical.

And the size of the craft maybe generates some kind of gravitation field towards the center? But people inside seem to be walking with some kind of fake gravity towards the floor.

True, but the Death Star is mostly hollow. At it's center is a large empty chamber that contains the reactor code, and then the structure is made up mostly of rooms and hallways. It would not weigh the same as an asteroid the same size. Also, if you were to stand near the center of the Earth, then which way is gravity? It's pulling you in all directions. So people inside the Death Star need gravity plating to pull them towards the floors, but people walking on the surface of the Death Star would be pulled towards the center.

If you made all the rooms and hallways curved around the shape of the sphere, then rooms near the center would not have flat floors. You would not be able to see the end of a long hallway, and stacking cargo would not rise upwards in parallel to each other. It would be more trouble and have no benefit. So creating flat floors that run parallel to the equator is more effective, and if all the floors are parallel to the equator then you need gravity plating.

Wouldn't it be better if it was shaped like any other space ship in most other Sci-fi's?

Here are some good reasons to make a large space station the shape of a sphere.

1. A sphere is the most effective shape for containing energy.
2. A sphere is the smallest volumn that will fit in a box of the same width and height, and therefore requires the least amount of materials to make.
3. To travel from one point to another point in the sphere is never greater than the diameter of the sphere.
4. Energy from the center core reactor can be distributed evenly to all points in the sphere.
5. A sphere is what nature would create (i.e. the moon).