Offset actually isn't purple - even though it is referencing another geometry, it isn't "attached" to that geometry directly because you can edit the distance it is offset.
I guess another good way to describe it would be that purple is the direct geometry from another feature. So if you make a line that starts on the midpoint of something NOT in the current sketch, that geometry is "projected" into the sketch, that way it is linked or referencing the other geometry.
You cannot edit purple lines
Purple lines will update when the object they reference is updated.
Purple entities act as if they are part of the sketch in that they can be used to constrain geometry.
Sorry if it's a little complicated - It's hard to explain well. Would you like me to make a screencast to show how they work for you? Maybe that would be the best option.
Also, I have never noticed that you can't offset an offset line. Though if you need to, you can just offset the original line again. I'll have to look into that some more.
Best,