The case is not only about the antenna; alternating electric and magnetic components create the electromagnetic wave that propagates along a line. Whenever the electric field grows, the magnetic field component diminishes, and so on.
Imagine the dipole like a thin glass tube in which a charge moves (say a small ball that can be an electron). As it moves toward the end of the dipole, the electric field grows (charge times distance) and the magnetic field diminishes. When the ball moves across the dipole center, the distance from it closes to zero and the electric field goes to zero; it the same time the magnetic field approaches its maximum. All such processes create a wave with a specific frequency. The wave propagates along a line normal to the dipole as shown in the right picture.
As the electric and magnetic field alternate in the normal plane to the line of propagation, they create the "transversal" field. To the contrary, sound as the acoustic wave is created by mass particles moving along the line of propagation; this is the "longitudinal" type of wave.
The No.3 of your question is the secret as explained above- the alternating electric and magnetic wave components in the elmag wave are not only orthogonal (normal to each other), but also orthogonal in time when the electric field comes to its maximum, the magnetic field crosses zero (intensity), and reverse.