After the cover is stripped, wash it & put in on a flat surface in the sun to relax mild wrinkles. A steam iron or heat gun ON LOW TEMP will relax severe wrinkles.
The loop for the draw rod is heat-welded together, so if it's tearing loose at the ends, there's not much you can do to fix it. Sewing will probably produce tears over time; most glues probably won't hold long and will probably warp or discolor the plastic; attempting to weld the plastic back will probably just burn through it.
HH66 contact cement might work.
Another fix would be to have an upholsterer duplicate it in convertible top fabric, but the material must be VERY thin to roll up inside the end caps.