After caesarean section 15 days, abdominal contraction can be done in bed, but the amplitude should not be large to avoid wound rupture. For example, lie flat on the bed, bend your knees (like doing sit-ups), forcibly lift your abdomen for 5 seconds, then restore your original posture and relax. Keep doing this, from less to more, try it first, and then increase it when you get used to it.
As for skipping rope and running, it depends on your physical recovery. I want to run three months after delivery, but the doctor told me that I can't run yet, and I should start jogging five months later. Anyway, I will do what I can, and I will never exercise to lose weight.
I wish you success in losing weight.