There are no control point coordinates, only the first derivative value for each point, and the length of resulting curve segments between each 2 points is given. In the simplest case, all curve segments should be of the same length.
Is it possible at all, and how?
Also, is it possible for 3D curve? For each point, there are 2 angles that define curve direction at each control point.
This curve is not supposed to have any knots and self-intersections. Angle change between points is not bigger than few degrees.
Yes, it is possible. You can construct a cubic Hermite curve meeting two points and two tangent directions with specified magnitude for the end tangents. Adjusting magnitudes for the end tangents will allow you to change the curve's length to meet the desired value.