Rebuilding the profile of the cornice is gonna be very time consuming.
If faced with that, I would make a profile of the cornice out of a thin material such as a scrap of laminate flooring and then use something like browning plaster and drag the profile over it to get a rough outline. Once dry, I would then use a decent quality filler such as
Toupret interior to build out the profile before sanding it back. You will probably need to apply a number of coats of filler though.
Alternatively, given that the damage is only on the lower part, wrap some plastic around a length of timber and screw that to the wall. You can then use that as a line to fill up from. The filler won't "stick" to the plastic (read: wood).
You will need profiled filling knives, at a push, a putty knife might work. I use palette knives for those kind of jobs.
Once the cornice has been fixed you can concentrate on the area below. I would recommend pouring some wood glue in to the cracks, the plaster looks loose. Wood glue often (but not always) helps to "lock" the loose edges. Then use the same filler, again you may need to apply more than one coat.
If you want, nearly dust free sanding, consider a
Mirka Handy Sander connected to a vacuum cleaner. Be advised that the dust will clog the pores in the vacuum bag pretty quickly.
Realistically, as a pro, I would allot about 6 hours (of labour) to restore that to its former state. It really isn't a straight forward job.