How many wave cycles exist in a photon? When we say a photon is a packet of energy with frequency of f, it means it consists of at least one electromagnetic wave cycle (otherwise we can not measure its wavelength).
Is there any experiment or theory that shows how many wave cycles exist in each photon? I am asking because besides the frequency, this number also can affect the energy of the photon (a photon with two cycles should have two times higher energy than a photon with just one cycle, while they both have the same frequency and wavelengths). This is a little paradoxical to me, because as far as I know the energy of photon only depends on its frequency.
 A: A photon has no cycles.     It's like asking how many fingers does an apple have.
The thing that oscillates and has cycles is the electromagnetic field.  The photon is an excitation of the field.  Roughly speaking, adding a photon to a field means increasing the amplitude of the underlying wave.
The size of a photon is a different question.  It doesn't really have size either, although one can say that the size is the same as the "cavity" in which the field is defined.  To explain that in detail will take us far afield, but take as an example a laser.  The cavity of a laser is the space between the mirrors, so we can say that the photons, or excitations of the cavity modes, are the same size as the space between the mirrors.  Once outside the laser, the cavity has no boundary.  We can approximate the light field in unbounded space by a plane wave which is boundless in all directions.  For that (approximate) picture, the size of the photon is infinite.  In reality, there are no true plane waves, so the fields are always of limited extent, although it can be very large.
