Hi @Anonymous,
Sorry it took so long for me to get back to you. I looked into this and I think I have an answer to most of your questions.
1.) To address your edit about moving the projected sketch: when you create a projected sketch it creates a link referencing it to that original line. You will then need to go in and break the link in order to move it. You can do this by editing the sketch that the projection is in, then right-clicking the projected line and select "Break Link". This can be seen from the following screencast at roughly the 10-20 second mark.
http://autode.sk/1Jty3tP
2.) By deleting your construction lines, I was then able to select your spline in one-click as a whole. NOTE: This will still create the abrupt point in the top-right corner of your offset. This just has to do with the way your geometry is. You can only offset that smaller so much before that rounded edge starts converging to a point. A few suggestions I would have is to either scale the spline up (so recreate the spline smaller and then offset it bigger by 24mm). Another suggestion (and perhaps more complex method) is to view the curvature comb of the curve you have created. You will want the comb to look as gradual as possible indicating a smooth curve. This may make a smaller offset possible. You can smooth the curve out by doing a few things. The first is to delete the tangent constraints that are around the curve in the top-right corner of your spline and replace them with a smooth constraint from the sketch palette. Also you can move around the tangent lines (which I show in the screencast below) in order to try and create a smoother curvature comb.
I know #2 was a lot to take in so I created a screencast below detailing how I went about those steps. I ended up learning a lot about sketches so I thank you for coming to us with this problem! It's a learning experience for us all!
http://autode.sk/1PUlIxZ
This screencast should show you how to perform all of the steps I outlined above in #2. Please note that when I was selecting my tangent handles (they were originally green and then when i clicked them they became blue and i could move them and manipulate them) I was just trying to show you that is how you do it. Please don't think that what I showed was a good final example of what your curve should look like! I was going fast to keep the screencast as short as possible 🙂
I know that was a lot of information to take in, but please feel free to ask me any more questions you have and I will try to answer them to the best of my ability. If this answered your question, please feel free to mark this answer as a solution so others can benefit from this thread as well. Also the link I'm posting below is a really good forum discussion about curvature that you may want to check out!
http://forums.autodesk.com/t5/design-and-documentation/when-using-smooth-constraint-why-are-curvatur...
Thanks,
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James Youmatz
General Adoption Manager | Informed Design