I never had any question from an employment agency. Just looking at my resume and asking me about my qualification ,experience ,and if I can stand the interview with hiring my manager.
In the flied of IT
I did help a lot of IT firms doing some technical interviews, I just ask if he can do the job, starting asking them technical questions, try to figure out your true and fake "Experience".
Most of these question above are HR. Most of HR poeple cannot even make decision to hire you.
For thank letter, you also can send it to Hiring Manager to figure out the resultant for the interview if you cannot wait for an answer.
Things are little different on other fields