Yes, the Count is crawling "lizard fashion" down the wall, and he is dressed in Harker's clothes.  The reason for this is because Dracula wants to give others the impression that Jonathan Harker has left Transylvania to return to London.  It will then be left as a mystery when he doesn't show up in England, and anyone who questions the Count, he will be able to have witnesses that will verify that "Jonathan" left the country some time before.  In reality, Harker is Dracula's prisoner in the castle.

Because Dracula is crawling down the wall "lizard fashion," he realizes that Dracula is supernatural in some way; no one human could crawl down the wall that way. He also realizes several other things, the most important being that the Count is up to no good, and that he has access to places and things he should not.