Is Avogadro's law applicable for atoms or just for molecules? I notice that online definitions of this experimental law always say, molecules or atoms.
From the Wikipedia article on Avogadro's Law:

$${\frac  {V_{1}}{n_{1}}}={\frac  {V_{2}}{n_{2}}}$$ The equation shows
  that, as the number of moles of gas increases, the volume of the gas
  also increases in proportion. Similarly, if the number of moles of gas
  is decreased, then the volume also decreases. Thus, the number of
  molecules or atoms in a specific volume of ideal gas is independent of
  their size or the molar mass of the gas.

In lumenlearning:

Key Points
  
  
*
  
*The number of molecules or atoms in a specific volume of ideal gas is independent of size or the gas’ molar mass.
  

This made me wonder if $n$ in the $PV = nRT$ can also be the number of atoms in that volume of gas. Taking a practical example, what is the answer to the following question?



  
*Statement (I):
   Atoms can neither be created nor destroyed.
Statement (II):
  Under similar conditions of temperature and pressure, equal volumes of gases do not contain an equal number of atoms. 


My question is, if $P$, $V$ and $T$ are equal, can we say $n$ (number of atoms) are equal? 
The answer given is that, no they need not be equal since only number of molecules will be equal. The gas can consist of a mixture of diatomic and triatomic molecules, we can have the same number of molecules but different number of atoms.  
From what I read on Kinetic Molecular Theory, the volume occupied by the molecules of the gas is negligible compared to the volume of the gas itself. This is the central assumption. So I guess the law applied only to molecules and not atoms or the generic "particles" as how some sites define it.
 A: The number n in the Boyle-Mariotte-Gay-Lussac gas law represents the number of moles of the considered gas. Mole is a measure of the number of distinct particles (molecules or atoms) of a substance. Avogadro's law states that the number of gas particles in a given volume of an ideal gas is the same for different ideal gases at the same pressure and temperature. It is related to the mean kinetic energy of distinct gas particles viewed as mass points. Thus Avogadro's law holds for gases consisting of molecules as well as of atoms. Examples for gases consisting of atoms are the noble gases, e.g., helium and argon.  
A: Your problem relates to the Ideal Gas law and Kinetic Theory rather than to Avogadro's Law alone, which is a deduction from the Ideal Gas Law.
In the Ideal Gas Law $pV=NkT$ the variable $N$ refers to the number of separate particles in the sample of gas. These particles can be individual atoms (eg atoms of the gas helium $He$) or diatomic molecules (eg molecular hydrogen $H_2$) or polyatomic molecules (eg ammonia $NH_3$) or even a mixture of different types of particles (eg air which is a mixture of $N_2, O_2, Ar, CO_2$ and smaller amounts of other gases). 
If the ratio $pV/T$ is a constant for two samples of gas (which defines what it means to be an ideal gas) then it is the same constant, and the two samples contain the same number of particles regardless of their composition.
In Kinetic Theory the particles are assumed to be point masses or hard spheres. Their structure does not matter, neither does their mass, as far as this equation is concerned. The key assumption (which is justified by the accuracy with which the theory applies in experiments) is that the particles exchange energy with each other indirectly, via collisions with the walls of the container, and thereby reach an equilibrium in which each particle has the same average translational kinetic energy, regardless of its mass or its internal structure.  
The structure of the particles and the composition of the gas mixture do matter when you are asking about heat capacity of gases, but the Ideal Gas equation tells you nothing about that. For that you need to know about other forms beside translational KE in which energy can be stored inside the particles of gas, such as rotational and vibrational energy. 
You ask about departures (error rates) from Avogadro's Law. More generally, gases depart further from the Ideal Gas law as the size of the particles increase. The 2 major corrections to the Ideal Gas law relate to the amount of space occupied by the particles, and the forces of attraction between particles. These are expressed in the parameters $b$ and $a$ respectively in the Van der Waals equation of state for real gases
$$(p+\frac{a}{V_m^2})(V_m-b)=RT$$ where $V_m$ is the volume of one mole (Avogadro's Number) of gas particles. Both parameters $b, a$ increase as the size of the particles increase, and the bigger these parameters the greater the departure from the Ideal Gas law $pV_m=RT$ and consequently also from Avogadro's Law.
A: 
I notice that online definitions of this experimental law always say, molecules or atoms.

The problem with just calling them all "molecules" and being done with it is some are uncomfortable with using that term for unbound atoms.  If you have a container of He, there are no "molecules" in it.
So when it says "molecules or atoms", it means "molecules or unbound atoms".  It's not trying to say that the total number of atoms within the different molecular species matter.  
A: No, it is particles, i.e molecules, not atoms.
Imagine two identical containers (the same volume) with different gasses added to each and allowed to settle at the same surrounding temperature. Add each gas until the pressures are the same.
Suppose one has O2 and the other He in it.
Since P,V,and T are the same, and R is a constant, both containers have the same n - number of particles.
But the O2 container has twice as many atoms at the He container, since each molecule is two atoms.
A: It refers to molecules.  If the molecules are monatomic (such as He) instead of containing multiple atoms (such as H2 or O2) it's the same thing.  When there's more than one atom in a molecule, count molecules.
