Why "specific contexts" ? The topics that you can talk about in a Turing test are endless, as well as the duration of the test.
Wrong in both senses. Anyway "contexts" meant the kind of social situation. i.e. Chatting over an IM as opposed to talking in person.
The whole point about the Turing test is that the test itself provides the definition,
Moronic and incorrect. So in your world someone can produce a test that defines intelligence as being able to play a perfect game of tic-tac-toe and that would be a reasonable definition of the term. Yeah, good luck with that. I said it better earlier, the test borrows from OUR implicit tools for judging intelligence. However the term "intelligence" (other than in your world of tic-tac-toe players) doesn't have a very good definition. So we don't really know how accurate it is.
If I discuss a problem with a co-worker, I also get a good idea of how intelligent they are, and if they understand the problem.
How do you know? What standard are you comparing against? How are you recording the data? What sort of tests have you done to determine the significance of the data you are collecting? Whoops...you're probably don't none of those things in any useful way.
There is no reason why the same approach doesn't work with a computer program.
A test that has some key commonalities with some other test is good reason to believe that passing one test means passing the other. However confusing a test for what it's testing for is a classic mistake.