Let's not sell Clara short here, isn't she is a High School teacher.
Naw, I think middle school is appropriate. Her student Courtney is series 7 was 13. Making her middle school age. All the kids look about that age.
U.N.I.T uses whatever resources it has to deal with threats and Clara being the most recent companion to The Doctor who is their major resource is someone they would call on.
Totally agree. They couldn't find the Doctor. Clara is the Doctor's companion so she's the best chance of finding him. She's been through a lot and isn't a bad person to call in to advise on the situation.
You still come to the problem of U.N.I.T. essentially existing and palling around with the Doctor since his 2nd Incarnation. That is more than 50 years and several Doctor's they've interacted with (2nd, 3rd, 4th, 5th, 7th, 9th, 10th, 11th and 12th) and yet they don't have a sufficient profile/pattern of behavior in order to adequate find the Doctor without the help of middle school English teacher. It's like Adama and Tigh going to Laura Rosalin for advice on how to deal with Cylons.