electromagnetism - Counting d.o.f. and gauge fixing $A_{mu}$ and $psi$ in $D$-dimensions

Setup:

Let us assume we are in $D$-dimensional Minkowski space-time where $D=d+1$. Consider a free Abelian gauge theory. Then the electromagnetic field will satisfy $$\partial_{\mu}F^{\mu \nu}=0 \tag{1}$$ and this means that $\partial_{\mu} \partial_{\nu} F^{\mu \nu}$ is identically zero.

Question:

1. 
   

   The gauge field $A_{\mu}$ out of which we construct the field strength comprises $D$ independent components (the indices take a value for each dimension). Then, why people say that the field strength comprises $D-1$ independent components? How is this counting being done?

   
   


2. 
   

   And why these $D-1$ independent components are the off-shell degrees of freedom? In what sense?

   
   


3. 
   

   Finally, what happens with spinors? How many independent components has a spinor in $D$-dimensions and how do we find its off-shell degrees of freedom?