some of this geometry is able to be created now, in fusion 360, i think the techniques to create it may be different, usually in the past with Catia Ive found that its more automated for some modeling / sketching tasks but the same results are not impossible to create in fusion now it just may take more steps. disclaimer - some might not be possible too...
extract is easy to do - just activate a new component and then use offset =0 (or sometimes with a small tolerance like 0.1etc ) in the patch tools to transfer your surface selections from any of your existing components / bodies etc used for reference into your new activated component. I use this a lot to build new matching components from others or copy bits to use for other complex interfaces between components in a design.
intersect - there isn't a easy ability to intersect two surfaces yet to generate an intersection curve - i initially found the icon confusing as it depicts this exact thing but doesn't deliver.
you can however use it (one of your surfaces possibly) to generate the inputs required for the intersection of two sketches which isn't the same but can be useful using an alternative method to get the same result.
connect - the 3D sketching tools (and creating mathematically good blend curves ) currently are pretty basic and not there yet. splines got a reasonable update just now in the March update but its not like using G2/G3 etc blend curves in alias between a number of 3D sketched curves.
polyline - creating curves from points (e.g. the output of some points from an equation imported in to a sketch to build a curve) is possible via a small free tool / script. I cant remember its name exactly from the top of my head right now but its possible Ive done it before just not recently (or one of the others may point it out before i get back to it) it will probably be in the free apps
parallel curve - the workflow for this may not be as simple as your used to but should be possible via other methods - do you have any images or non proprietary examples you can share?
project - there are a number of projection tools in the fusion sketching tools that enable some pretty awesome results. combined with extract above it can be used to make some complex 3D forms.
Ive seen some complex chassis designs for water trucks in the past, but it was a few years ago, it would be great to see some examples to try out whats possible with the current tools.
the model in the example image you have shown is probably possible now using the method described above for extract and then using trim in the patch tools & thicken perhaps.
cheers,
Carl