First, welcome to the forum.
There are more knowledgeable people here then I, but I'll start.

1) Yes, they do make non-stabilized sticks......they are called HTH duration.....
they are very expensive and have less chlorine in them then tri-clor tabs. The best non stabilized chlorine you can use is just plain old bleach.

2) If you have a cya level more then 100, you must have a FC level at least 8ppm to keep your pool safe. The higher your cya, the more chlorine is held in reserve and the less you have doing the job it needs to.

You must go out of town a great deal to have a cya level that high.

Frank D.