Hi @JetForMe,
Reading back through this post, I think that there are some basic concepts that are not as clear as they could be in Fusion, combined with some unfortunate naming conventions that are the root of the problem.
I think the main misunderstanding here is the word "construction". There are two separate concepts involved here, both which share that word.
construction geometry. I prefer to call this "work geometry" (which is what it is called internally, but that's a different story). There are 3 types of construction geometry: work planes, work axes, and work points. They are created using items from this menu:

These objects create separate items in the timeline:

And create items in the browser:

as you can see here, the origin items are also composed of construction/work geometry.
construction/work geometry can be used in creating modeling features. You can create a sketch on a work plane, you can use a work axis in the Revolve feature as an axis of revolution, etc.
sketch construction curves. As you know, sketch is a little island of functionality itself. You create a sketch, you edit a sketch, while you are in sketch mode, your focus is creating and editing items in that sketch. Sketches contain curves (including lines), points, constraints, dimensions, text, etc. A sketch does not contain work planes, work axes, etc.
Within the sketch environment, a sketch curve can be a "construction curve". This is just an attribute on a curve that changes its appearance and, to some extent, its behavior. The construction attribute of any curve can be toggled using the sketch palette when a curve is selected:

or by right clicking and choosing the "Normal/Construction" command:

When a sketch curve is marked as construction, its appearance is changed to dashed:

And, sketch construction curves do not particpate in profiles, paths, etc in features. That is why, in the above picture, there is no shaded region that can be extruded. That, in fact, is the main reason why sketch construction curves exist - to limit their participation in consuming features. In every other way, these behave identically as "normal" sketch curves. You can dimension and constrain them identically, etc.
The last concept that is probably relevant, as @NicolasXu mentioned is "Projected Geometry" in a sketch. The Project command allows you to project the geometry from other objects into the sketch. You can project model edges, sketch geometry from other sketches, or work/construction geometry onto the sketch plane. The "Inculde 3D Geometry" allows you to bring arbitrary 3D geometry (including work/construction geometry) into the sketch world as 3D objects, where they can be referenced.
So, with these two concepts defined (and hopefully my definition is adequate), can you re-state your question? What is it you are trying to achieve? I believe that whatever it is, most likely there is some way to do it in Fusion. We'd be glad to help illustrate it.
Jeff Strater (Fusion development)
Jeff Strater
Engineering Director