OK, I spent some more time with this today.
There are multiple ways to do this type of design, and I think eventually you will find a path that works for you.
I focused again on Sketch10, because I think that at least some of the problems are revealed there.
Some of the problem is that your sketch is not very well tuned to accept updates such as you gave it by lengthening the lifter finger or lifter finger assistant. Some of this, unfortunately, does kind of require a sense of how the tool works. For instance, the way that projected edge geometry works. When a sketch updates, the first thing that it does it to update the projections, and then it updates the rest of the geometry that may reference that geometry. Second, you will need dimensions to control the distances to the references so that your sketch updates in a predictable way.
For instance, just taking one example. In this design, if I start just looking at sketch10, this is the starting point:

if I update d40 to 24 mm, the following happens:

I assumed that you really wanted this sketch to update. So, I looked at the sketch, and the cause was that the circles here were not projected edges. So I edited the sketch, deleted the circles, projected edges and completed the circle.
Then, I can edit d40 to 24, and I then get this:

So, we are closer, but as you can see, we still have problems, because, while the circles now update correctly, the rest of the sketch does not. So, I undid the parameter edit, and went back in to make some more changes:
I had to hook the vertical lines to be coincident to the points on the circle, and add some dimensions. Now, I get much better behavior on that side of the sketch

Now, however, I looked at the other side. Here we have a problem. This side does use projected geometry, both to "lift finger assistant" and "Rotation mount". So, when I update d47 to 24mm, I get this:

Mostly, it updates as I expect. That one circle puzzles me, and may be a Fusion bug. But, the main problem here is that this sketch references geometry from the "Rotation mount" component, which does not move when d47 is edited. So, now, the geometry of the component being built from sketch10 is going to be a bit wonky.
This is where there are a variety of design approaches that could be applied. If you can get the geometry in "Rotation mount" to move with d47, then this approach can work. Or, you can build components in a different order. The idea here would be to build the "lift finger" and "lift finger assistant" components, then this component (I think it becomes "lift finger parallelogram"), and then build "Rotation mount" from that geometry, by projecting edges from "lift finger parallelogram" into "Rotation mount", so that you have a chain of dependency that works well together and tolerates updates. All of these are kind of "top/down, model in place" approaches.
Or, you can use a different approach entirely, and create components not in place, relate them with joints, and use Combine to do things like cut out the notch in the "lift finger parallelogram" where "Rotation mount" fits in.
Anyway, the net takeway is that some of this takes time and experimentation to get right, and a bit of planning.
So, good luck with your designs!
Jeff
Jeff Strater
Engineering Director