How was Obito able to use Kamui immediately after awakening his MS? In Episode 435 of Naruto Shippuden, Obito awakens his Mangekyo Sharingan and attacks the hidden mist ninja using the MS ability. However, he had no prior knowledge about the MS as Madara never explained it to him at this point.

So, how did Obito know about the Kamui Dimension after he suddenly awakened his MS? Madara never said that it can be a MS ability, nor Zetsu told him anything.
Also, Kakashi figured about the Kamui much later. How did Obito figure out how to use the ability without training?
During the fight against the Hidden Mist ninja after Rin's death, he never teleports his entire body to the Kamui dimension. His intangibility ability is probably activated involuntarily (he never got attacked unless he purposely made himself tangible, like the fight against Minato). Kakashi doesn't have intangibility, so he wouldn't know how his MS worked until he figures out how to use Kamui.