Hi gillesht,
so now that Jeff was able to help you identify why you couldn't edit your "spline", thanks Jeff!, I'll show a way so you can get to the result you really want.
One of the big problems with using projected or duplicated edges is the software will add as many points as necessary to replicate the shape. This is not exclusive to Fusion, every modeling software I've ever used does this (and I've used quite a few) and without user intervention, know how and powerful tools it's nearly impossible to get a quality curve from copied geometry; and if you have a poor quality curve that will lead to poor quality model surfaces. I'll show you what I mean throughout this post.
Back to your design:
so I took a look at the curvature comb of your sketch and the quality of the splined shape is quite poor; this is the result of the software as mentioned above.

here is the result of that projected curve. I can tell you from experience that there are a bunch of points underlying that curve, even though they are not visible, which is why the curvature comb is so rough. The curve looks ok, but the quality of the curve is very poor, the best way to fix this is to build a new sketch and you get to control the number of points in your spline as well as edit your spline to make and adjust the final shape you truly want.

I redrew your sketch and applied dimensons to everything; again, this about controlling your design. Dimensioning is not necessary, but makes editing easier especialy if you have particular parameters that your design is bounded by.

I'm referencing your orignal "spline" as a construction curve to build the new spline to. I also added extended construction lines with a smooth constraint to the "spline", this will aid in the end conditions of your new spline matching the referenced one.

Now I've added the new spline, with just two points and snapped the handles to the extension reference construction lines, again giving an almost perfect match of the end conditions of the orginal "spline". Adjusting the length of each spline handle you can closely approximate the orignal shape.

I worked the two point spline and was not able to get as close as I wanted to the referenced "spline", so I added an internal point and was able to get really close.

If I turn on the curvature comb of this spline and compare it to the original "spline" you'll see a huge improvement to the quality of the curve.

vs.

a little bump in the comb of the new spline, but it's very smooth, some time and tweaking and you could work most of that out. This is where striking the balance of mathematical quality in your model and your final products quality (based on materials, finshes, manufacturing process, etc.) is a judgment call on the designer. If you are designing something with a really smooth glossy finish, like a car body, this likely will not be good enough, but if it's something that will have a matte or textured finish it may be okay. It's really up to you to decide.
Now we have our finished profile we can revolve our shape.

One more comparison now of the original curve vs the new spline, but as it manifests itself in the models surface
This time we'll look at some zebra stripe analysis of both models
First the original. you can really see how the poor quality curve affects the quality of the revolved surface. The stripes are really rough; this is the direct result of modeling from a poor quality curve input.

Compared to the new spline where we controlled the curvature of the spline. You can see that the surface quality of the revolved shape is much nicer and smoother when we start from better source geometry.

We can have a much deeper conversation about model and surface quality, I know there are a number of designers on this forum that have strong points of view about quality. If you have not read it, I highly recomment reading Gray Hollands Periodic Table of Form, it's a really great piece on form and quality and perception of products based on the designers intangible intent and the engineers rational intent, both important and both influencing final product quality.
hope this helps.
hope this helps,
Jamie Gilchrist
Senior Principal Experience Designer