BC₁ shows spring with the lid fully opened. It is always the maximum length of the spring. All of the other real-world dimensions are based off of this. As such, it is impossible for it to be "out of limits". There are some absurd locations for it, but it is impossible for it to be out of limits, as it is a constant.

I don't believe that there is any way to prevent you from moving a point outside bounds. Well, there is (the point with the vectors is required to be on the circle with center A and radius AC, for example), but I can't think of a way to do it in this case.

AC and AC' describe the edge of the lid. Chances are that the place you're mounting the spring to the lid is not on the same plane as the edge of the lid; that is, that the lid is really a shallow box and not just a flat piece of wood. C₁ and C'₁ are points that take into account how far into the lid box you'll be mounting the spring. If you really will be mounting it flush with the edge, move the l slider to zero, which will make the sub-1 points coexist with their masters.

Um…. As you move the box end of the spring closer to or further from the hinge point, the lid end also has to move. Imagine a non-compressible rod. If you have the lid propped open and you held the rod in the same location as if it were a spring and then you moved the rod further into the box, the end of the rod at the lid would move closer to the hinge.