First off, the "series of straight lines" is due to the ACIS Quality setting being the default 50. Change it to 100 and everything will be smoother.
Second, your outer cylinder has been hollowed out with a cone (or formed by lofting with different diameter circles on the inside at each end). The thickness of the shell at one end is somewhat different than at the other end (the outer diameter remains the same). If this is what you want, then fine, but it makes doing what you want difficult.
Creating a hollow cylinder and subtracting it from that portion of your object is a workable idea, but I would use it as a template for creating the new hollowed out cylinder first. Note that, while you may be tempted to use the Extract Entity / Extract face from body command, it will increase the size of the holes as they are scaled outwards due to the curved surface. Then, use the Shell Solid command to make it the desired thickness (unless you need a sloped inside surface, then you'd have to create that as you did before).
For subtracting the current cylinder, I would make the duplicate just a bit wider and longer so that it completely envelopes the part you want to remove so that there is no detritus left over. I would then use the Shell Solid command to the desired thickness to remove the cylinder, but not a lot of the other stuff.
Following that, you will have to make straight slices at the ends of the 'spokes' (or whatever you're calling them) so that you can extend them without them scaling (due to their curved surfaces). I did it by setting World view and rotating that view 45° by using the Shift and one of the cursor keys twice (22.5° with each press). This made it easy to draw perpendicular lines to use as guides for 3D Slice.
Before you extend the spokes, you'll have to prepare the hollowed out sections of the outer ring.
The teardrop shape'd hole can easily be duplicated by using the Extract Entity tool (select Extract Edge with the Extract loop from initial edge and face option active. One of the last things you will do is 3D Subtract that from the new outer ring. You can see it in the attached drawing.
The conical indention seems flawed. I don't know if you wanted the hole in the face to extend through the outer ring, but it has two tiny holes left over from the intersection. As is, you cannot use Quick Pull because the slope of the indention will expand out, limiting the extent (see attached drawing). Extrude 2 Face will fail for the same reason. Eliminate the indention, extrude, then put it back.
That should pretty much cover it. I could have done it, but I don't know the increased diameter or the actual thickness profile (as described earlier).
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