I'm surprised by the rapid succesion of the interviews. When I applied for an internship at Google, I think the entire process lasted about three months until I got a final acceptance email. Only had 2 technical phone interviews spread over a month period and they were both decisive (aka if you failed the first one, you didn't get in the second one).
This was quite a contrast to my Facebook experience, where I had a contract signed after I think 3 weeks. :)
I'm really quite surprised that binary search is considered difficult, have you ever tried to implement quick sort? I can write AVLs with less bugs than quick sort.