Is the combination between point reflection (https://en.wikipedia.org/wiki/Point_reflection) symmetry and hyperplane(or axial using Hodge duality) reflection symmetry (https://en.wikipedia.org/wiki/Reflection_symmetry) in $\mathbb{E^4}$ possible for a given orientation of $\mathbb{E^4}$?
I think point reflections for point $P$ in $2n$ dimensions give 180º rotations in $n$ orthogonal planes intersecting in $P$ that preserve space orientation.
I think you're asking whether hyperplane / axial reflections in $\mathbb{E}^4$ preserve orientation. If that's the question, then the answer is no, by a very standard argument: after conjugating by a rotation if needed, those reflections can be written in matrix form as $\mathrm{diag}(1, -1, -1, -1)$ or $\mathrm{diag}(-1, 1, 1, 1)$. Since the determinants of these matrices are $-1$, they both invert orientation. (By contrast, note that the point reflection matrix is $\mathrm{diag}(-1, -1, -1, -1)$ and thus preserves orientation, just as you suspected, since the determinant is $1$.)