Someone helped me to make a cross-section of a tire the other day, and his curb looks like the bottom picture (in edit mode). I tried making another BezierCircle but when I get into edit mode it looks like this:
So how can I change that into this?
Alt+C to toggle cyclic. If you change the handle type (V) to ‘free’, the handles won’t move when you toggle cyclic. You could also delete a segment between two handle points by selecting them and X -> segment.
What JA12 says is true but if you want to clean “the clutter”, you must do a little more…
In the [N] panel, you can disable the normals and the handles. Switching to 2D also automatically disable the normals (but I’m starting to think it shouldn’t happen). You can’t see the type of the control points any more but everything else keeps on working: [G]rab, [S]cale and [R]otate.
And last, don’t forget to reduce the Preview Resolution if you don’t want to end up with tons of vertices when you convert to mesh. 
Thank you :). I was talking about the clutter because I wanted to get rid of all those arrows and such but disabling handles + normals did the trick.