Given a variety $X$ (possibly singular), and define $\Omega_X^1$ to be the sheaf of Kahler differential on $X$. Then is the sheaf of i-forms $\Omega_X^i$ ($i=1,2,...$) an $S2$ sheaf (i.e. it satisfies Hartog's phenomena, in particular, the sheaf is determined by its codimension-1 behavior)?
Also, let $X'$ be the smooth locus of $X$ with inclusion $i:X'\to X$. Is $i_*(\Omega_{X'}^i)=\Omega_X^i$ in general?