I too am American and I've been here for several years. I love it. I do miss mountains and more green but we all take the good with the bad (and thats why we have vacation:) )
I'm like you with the call to prayer, its a very comforting sound actually and when I go back home, I miss it.
The family and traditions tie back to generations we would not be able to necessarily recognize in such a young country and culture.
So yes, Hail to Qatar. We love you and enjoy spending time in this great country.
Now if you could arrange something like a big air conditioned bubble over the country during July and August (like The Truman Show) , I would be forever indebted. :)