WMG / Being Erica

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.
  • One of the doors in the group therapy room certainly looks like it's got roundels on it...

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.

Doctor Tom's daughter Sarah is a Project Leda clone

This may also account for why it was so difficult for Dr. Tom to find her: either Sarah Manning accidentally erased Sarah Wexler's records while trying to conceal herself from a con gone wrong, or Dyad abducted her to do more in-depth studies on her after she ran away.