Doctor Who Movie

Ok, so I decided tonight to rewatch the Doctor Who movie. I realised I hadn't watched it since it first came out! Anyways now I'm bothered by two things.

First, how did the Master get into the TARDIS before the kid? He didn't have a key, and he didn't take the spare because it was there when the Doctor needed it. (Sif hidden spare anyway)

and Second, what's with all that stuff about the Doctor being half human anyway. Are they pretending it was never brought up? 'La la la I didn't hear anything, I had my fingers in my ears'...