Q1: A simple dipole antenna emits radiation most strongly perpendicular to the axis of the antenna. It emits very little out the ends. The antenna has no power variation in the circular direction around it's "waist." (This is simply the nature of electro-magnetism.) This radiation pattern matches the most common usage pattern -- the various other receivers/transmitters are situated at about the same height when the antenna is oriented vertically. When you factor in that dipoles are easy to construct (they are physically simple structures and electrical systems), they become an obvious choice.
Q2: What you suggest is exactly a dipole antenna. Note that a textbook dipole antenna is TWO wires, in a straight line, with the transmitter/receiver connected to the near ends of the wires. If you just have one wire, with a trans/rec connected to one end, you still have (in term of the E&M theory) a dipole antenna -- it's less efficient, but even easier to construct.
(Note that I'm really glossing over the E&M theory here. In reality, a trans/rec has two connections by definition. Whatever is in the trans/rec has two electrical sides. For best efficiency, you connect them to the two sides of a dipole antenna. You can leave one side disconnected -- but that's just a really small second side for the E&M purposes, giving you an unbalanced antenna. An example of a really cheap dipole setup was the older car antennas: Straight wire sticking up, with the radio receiver connected to the wire and the other side to the car's ground. So the whole metal car was the other side of the antenna.)
Q3: That cisco page has information on different types of antennas. An omni directional antenna would be as you described: The distance from the antenna for a given intensity would be a circle. (The pattern is called a Toroid.) The diagram you're asking about shows a varying distance from the antenna for a given intensity -- that pattern is often said to have lobes. The advantage of that antenna is that it is better in particular directions; Notably, it's primary lobe is significantly better than it's other lobes, making it work much better in one direction, thus is is more or less unidirectional.