It would be nice to see where things currently stand in your model. So if it’s at all possible, please post it up so we can know what you have without having to guess.
Otherwise, starting off from scratch… If I were to model this object, I think I’d do a bit of design work for how the layout of the varios cross-sectional areas are suppose to look. Once decided upon I’d group that geometry together so that it can be used as a template/jig for constructing the main model.
*[ If you don’t already know about how and why objects should be Grouped or, turned into Components (because as you say you’re relatively new to SU)… then make sure that you go through one of the tutorials so that you see how groups/components are suppose to work.]
Circles within SketchUp are made up of flat segments. . . and you can control how many segments, or Sides, your circles have. Use this fact to your advantage… And take a look at the Entity Info’ window, so that you can make changes to the side counts of circles that have already been drawn should that be necessary.
You can (and probably should) use a value which is evenly divided so that your chords fall into the right positions. And its often a nice strategy to reduce the side count value down so that you can easily identify certain alignment points within a circle… (e.g., you can have a 3 or 4 sided circle, just long enough to set up some guidelines for (triangular, 120º; or square 90º reference points,. . . and then reset the side count back up to whatever you wanted it to be once the guides are in place)… better still just draw in a secondary circle to use as an alignment aid/jig with the side count set to whatever you need.
When snapping your rectangles onto a Circles Edge Segment. . . make sure that you’re locking onto the End Points or Mid-Points in a consistent manner, so that you have even symmetry built into the model. Zoom in if necessary so that this is all fairly clear.
[. . . this is the main reason I’d be doing a little cross-sectional study just to work out how I’d like things to be placed.]
Rotating a rectangle into alignment with a circles chord isn’t too tough, but it might be if you’re not too familiar with how the rotate tool works… so I’m not really sure where you’re having problems from a modeling standpoint. I’m not sure, but again it’d be nice to see your model if possible.