The Doctor and The Master to be friends? - Jon Pertwee (The Doctor) and Roger Delgado (The Master) were friends in real life, that explains their on screen treatment of each other. Jon Pertwee was devastated when Roger Delgado died in a car accident. Was apparently one of the reasons he left Doctor Who when he did.
As for 10th Doctor and and the Master, the Doctor believed for centuries that he was the only surviving Time Lord, so of course when he discovered one alive, no matter how evil he was, he didn't want to see that other Time Lord die.
Series 9 to Adress Mystery or Capaldi's Reappearingf Face - I haven't seen Torchwood so haven't seen his character in that, but some people commenting on the article say the previous producer claims Capaldi's two previous characters are related. The Torchwood one being a descendent of the first Doctor Who one.
Jemma Redgrave confirms return to Doctor Who (episodes 7 and 8) Peter Davison (5th) Doctor Interview 11 incredibly British things on Doctor Who explained