The physical design of a humanoid robot? No; Asimov's designs would constitute prior art (not to mention the existing real-world humanoid robots, or even humans themselves if you want to get existental). Any novel mechanical workings that make a humanoid robot possible would certainly be patentable, however.

Yes, they certainly shouldn't! They can patent the inner working of the robot that they came up with, but they can't patent all possible humanoid robots, regardless of how they're implemented on the inside.

  should they be unable to patent that invention

Of course not, they didn't invent anything.