Trip and Malcolm find out that the results of their actions may have unforeseen consequences in a particular universe. Trip finally talks with the mysterious Rose and discovers what has happened to the Doctor. The final showdown with Future Guy is on the horizon.
Spoilers: ENT "Countdown", "Zero Hour"
The TARDIS materializing around its occupants happened (albeit in reverse) in DW "Blink". "Do you two wanna be alone?"
In DW "School Reunion", Rose Tyler meets Sarah Jane Smith, a previous companion of the Doctor (Third and Fourth, to be exact). The two women compare notes about their Doctors, and both find out he still talks to the TARDIS like it was his girlfriend. Rose makes this remark and Sarah Jane bursts out laughing.
In DW "Turn Left", Donna Noble makes a decision that alters her universe, where the Doctor died. The TARDIS is later stripped for parts to send Donna back to that point in time to correct it. The TARDIS had basically given up and "died" along with the Doctor.
DW "Rose": The first word the Ninth Doctor said to Rose Tyler was "Run."
In "The Eleventh Hour", the Eleventh Doctor tells the Atraxi, "Hello, I'm the Doctor. Basically...run."
DW "The Waters of Mars" The Doctor saves a woman who was supposed to die, and in doing so, becomes drunk with arrogance and power. He declares "Time is not the boss of me." The woman later dies by her own hand to restore the time line. The Doctor realizes his hubris, but he knows his time is almost up..."Time Lord Victorious"
is what he calls himself during his delusional state.( Chapter Ten: The Road to Hell is Paved with Good Intentions )