As a freestyler, I never liked skating forward if I could help it. Backward skating is faster, stronger and more fun since it's easier to use both legs at once. Forward stroking is done one leg at a time and you have to watch the (wait for it...) TOEPICK!
I use "curve" to describe the shape of an edge tracing. As in "Shoulders over the curve," "Stay on the curve," and "Lean into the curve."
I use "lobe" to describe a curved step or series of edges, mainly on Moves patterns. Each half-circle pattern is a "lobe."
Most beginners prefer inside edges and turns because it's less scary - you can press on the arch of the boot and put your foot down if you chicken out.
Edges and turns in your natural direction (CW or CCW) will always be more comfortable, but practice strengthens the weaker side and it can be evened out.
If you look at your tracings, you can see if you are truly on an edge: there will be one thin line etched onto the ice. With control, you can skate on a very shallow edge that appears to be straight, but the easiest way is to skate on "flats." When you're skating on flats, both edges touch the ice and leave a parallel tracing. (I can testify that a skater can trace a curve on the ice using both edges...it's called "double tracking/tracing" and it's wrong.
Ask me how I know...)
Being able to skate on deep or shallow edges is a skill that School Figures used to develop, so practice controlling small and large circles to DIY.