Without going into a full kiltmaking lesson and giving away all our secrets, yes, Steeking in a Contemporary Style Kilt shows up as a horizontal line of stitching at the hip line.

Other than proper apron taper, the Steeking line is the single most important thing a kiltmaker needs to insure he never skips.

13 oz. Cotton is exactly the same weight as 13 oz. Wool. Which is considered Mid weight Kilt fabric. The Fell will get thick and "Pillow-Butt" without removing the excess fabric.

The strip I think you are referring to is the hair canvas used in Traditional Kilts. Yes, it is a strengthening to keep the stress away from the taper stitches.
The best analogy I can give is, - you wear the reinforcement, the kilt floats over that without pulling. Just as a proper jacket which has interfacing. It is the interfacing which is sized to you and what you wear, the outer fabric of the jacket floats over that and will not pucker or pull.

In a kilt the hair canvas is built in and is continuous and connected to the straps and buckles. This is where all the stress is taken up. The Tartan fabric and pleats simply hang from this internal belt.