Can I say that $E[X | c] = E[c | X]$, when $c$ is a constant and $X$ is a random variable? $X$ is a random variable defined in a sample space
$c$ is a constant $\in R$ (real numbers).

You cannot condition on a constant, so I guess you mean constant random variable. A constant random variable is independent of any other random variable, so
$$
E[X|c]=E[X]
$$
So you're asking if $E[X]$ is equal to $c$s value.
