Being Erica/WMG

The reason Kai can't find Erica in 2019 is because she's a therapist at that point.

Thus she no longer exists in the 'real' world in the sense of having an identity that he can actually find.

• • More than likely confirmed by 3x12, "Erica, Interrupted".
    • Sort of Jossed by Episode 4x08, "Please, Please Tell Me Now". Dr. Fred tells Erica that she really is dead in 2019, following a subway bombing that kills her and many others. But then Erica receives a visit from her future self, and learns that there are alternate realities. Erica's life seems to diverge into two branches upon the losing of her virginity: one timeline is where she is still alive in 2019; the other is where she is dead. Unfortunately, the reality where Kai is from is the one where she's killed in the bombing.

Doctor Tom is The Doctor.

And I didn't even say "X is a time lord" ... ("facepalm") Just think about it. He is a DOCTOR! He travels through TIME AND SPACE! His office is BIGGER ON THE INSIDE! (my theory is that his office IS the doorways that Erica walks through)

• • He also carries a water pistol (Episode 3x01, "The Rabbit Hole), just like Ten.
• Alternatively, the Doctor was the original therapist.

Erica's voice overs are things she's saying to other people when she's a therapist.

The voice overs seem to speak in an older more experienced fashion and almost in a more teaching fashion as if she's telling people things.