(a) Dunno the requirements for kyo sa nim...just know the test is mega-hard and endurance-intensive. the requirements, then, are probably everything and anything up to e dan rank. It's not like it's something you see posted on the wall. You have to be recommended to be able even to take the test.
(b) Sure. Lemme just scan the manual. Now, mind you this is an old manual, from when I first started, so some minor things may have changed. This is how it was when I was a gup level, though, and IIRC there haven't been any major changes, at least not in the hyung requirements. Also note that my mom scribbled in a few things on the one page.
Hyung Requirements
Il Soo Sik, Ho Sin Sul, and Kyok Pa requirements
There's also always sparring, one-on-one, as a requirement. In my day, we weren't required to wear pads for this, but nowadays they probably do, at least for gup levels (we don't for dan tests/recertifications, at least).
I think I may have posted this before, but here it is straight from the manual c. '99/'00.
Tang Soo!
Okay, let me try and clarify a few things...
JT - your curriculum is very traditional. In fact, most people would recognize that as TSD if they knew what they were looking at. This method of teaching isn't Korean, however. It's Japanese. In Shotokan, the root of TSD, one practices Kihon, Kata, and Kumite. Those are the three pillars. As a step between kata and kumite, one steps that included striking and grappling techniques were inserted.
What we do is very similar to this, except, I take a brick and morter approach. What you practice as kihon (kicho), I see as parts of kata. Not basic techniques. Basic techniques are things like strikes, blocks, locks, throws, pins, etc. There is not a lot of discussion about what basic techniques should look like other then technical points that make it work. We practice on pads, with partners, and with contact.
Kata shows you how to put basics together. It gives you combinations and responses to try. It shows you how and where to strike the body. For me, a technique like "gedan barai" or "hadan mahkee" is showing you a particular way to use the kihon that a student is learning.
We then incorporate that in drills and then we turn it into sparring. Thus, everything is connected at every step.
What you are doing is different then this. "Hadan mahkee" is hadan mahkee. I think you realize that it can be something else, but when you practice kihon, it is hadan mahkee. That is your focus when you are doing kicho. You aren't looking or practicing what it really was intended to do. Solving that dilemma was a years long journey for me. I didn't like practicing like that. I wanted to have what we did in basics, forms, drills, and sparring to directly build off of one another and philosophically/technically make sense.
This has not been an easy process on me or my students. I've revised my requirement sheets several times in this effort and at times they grew very frustrated in me. Now, though, I think they can see the value in what we are doing. Especially when I include the fact that this approach is historically more accurate to how te was taught.
See what I'm saying?