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: 
The answers are good, but I need to explicitly state what is conceptually wrong in your question.

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

The classical electromagnetic wave is one wave, its intensity and direction depending on two variables that are a function of each other through the solutions of [Maxwell's equations](https://en.wikipedia.org/wiki/Maxwell%27s_equations). A simple functional relation of **E** to **B** is seen in the [plane wave solutions](https://en.wikipedia.org/wiki/Sinusoidal_plane-wave_solutions_of_the_electromagnetic_wave_equation#Plane_waves)

[![E and B ](https://i.stack.imgur.com/Hka8A.png)](https://i.stack.imgur.com/Hka8A.png)

> 
> How many waves are there for a particle wave?
> 
> 
> 

As stated in the other answers, the waves in particle representations are **probability waves** and depend on the solution of the quantum mechanical equation and boundary conditions of the given interaction.

> 
> 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
> 
> 
> 

The photon is a **point** particle in the [standard model of particle physics](https://en.wikipedia.org/wiki/Standard_Model) and is the quantum of the classical electromagnetic wave. It can be proven that the classical wave is a superposition of a large number of photons, and also this is seen experimentally, [see here](https://www.sps.ch/artikel/progresses/wave-particle-duality-of-light-for-the-classroom-13/).

> 
> for an electron: one wave or two waves?
> 
> 
> 

There is one wavefunction for each particle depending on the boundary conditions and the interactions, and it gives the probability of observing the particle.
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.