Question: An electromagnetic wave is made of an electric wave and a magnetic wave, so 2 waves.

How many waves are there for a particle wave?

* for a photon: if it is not made of two waves, then I don't understand how the photon wave could be compatible with the electromagnetic wave
* for an electron: one wave or two waves?

Answer: 
For a particle propagating through space, its wavefunction furnishes the *probability of finding it in a given place* which is a different number for every different place. This is a single-valued variable.

Electromagnetic waves are very different; they propagate through space as the interplay between a linked pair of an electric field and a magnetic field, and so a *wave description* of the photon requires the specification of both the electric and the magnetic fields at a single point in space as well as their respective rates of change.
Actually in electro-magnetic wave there is effectively only one "wave", because the electric and magnetic components are strictly coupled. (Not only in waves, but also in general.) Also photons and electro-magnetic waves are the "exact" same things. The names are only distinguished to emhpasise if we are talking about the particle properties, or the wave properties of the same thing.

In particle "waves" there is no physical field that oscillates, but only probabilities. ("In the particle waves a number oscillates.") Thus it is more convenient to talk about a **wave function** of a particle, rather than a particle wave.
Also a particle is usually described by a wave packet, and not by a single (sinusodial plane) wave.