The Reference Desk/Second Doctor: Console/The Master

From Tardis Wiki, the free Doctor Who reference

What I'd like to know is:

  • How the Second Doctor knows who the Tremas-Master is in "The Five Doctors"? He didn't show up until the Third Doctor era, and the First Doctor didn't know who he was.
  • Why does the Second Doctor operate a TARDIS console (as well as the room itself) that wasn't his in "The Two Doctors"? I know the real-world reason, but what is the in-universe reason. And how is he suddenly able to steer it properly?