This cant be the case because obito would've figured it out, he not only has senju DNA but he had 16+ years to train his eye, you cant possibly say he hasn't discovered kakashi's kamui yet and considering hes seen kakashi use it, it just doesnt add up how he wouldnt know how to do it. Therefore he doesnt have it, and as for the whole "how can he warp his head" thing, someone explained it on the last page, if he focuses he can change the size of his kamui vortex. However its still in his line of sight. Just think of it like the game portal, he used kamui through his eye to create a vortex or "portal" in which he used to slip through
EDIT: in fact he probably cast kamui on the floor and fell through because he was looking down when he came back