Variation of Arrhenius equation with concentration
The Arrhenius equation gives you a rate constant $k$.  

For a second order reaction, $k$ has units of $1/Ms$.

For a first order reaction, $k$ has units of $1/s$.

The Arrhenius prefactor $A$ has the same units as $k$.  

The rate, as opposed to the rate constant will depend upon concentration. For the first order reaction, the rate constant is multiplied by one concentration to get the rate, and for a second order reaction the rate constant is multiplied by two concentrations to get the rate.

If $k$ and $A$ do depend upon concentration, that would imply that the reaction is not accurately modeled by the rate constant (for example not really first order when you are modeling as first order or not really second order when you are modeling as second order).

As far as activation energy $E_a$, the equation can be written in terms of energy per mole divided by $RT$ or energy per molecule divided by $k_BT$ (where $k_B$ is Boltzmann constant).  $E_a$ does not depend upon concentration.