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).

No to the question in the title. It can happen but that is a special case.

If $c$ is looked at as random variable defined on the same space as $X$ then $\mathbb E[X\mid c]$ is a random variable that can only take one value. This because by definition it is measurable wrt $\sigma(c)=\{\varnothing,\Omega\}$.
Further its expectation must equalize the expectation of $X$.
These two facts together leave only one choice: $\mathbb E[X\mid c]=\mathbb EX$.
Further we have $\mathbb E[c\mid X]=c$ because $\sigma(c)=\{\varnothing,\Omega\}\subseteq\sigma(X)$.
That together tells us that: $$\mathbb E[X\mid c]=\mathbb E[c\mid X]\iff \mathbb EX=c$$
