Experts and BHG readers answer.
You can cut coneflowers all the way to the ground after they have died back for winter. Or if you prefer you can leave them in place over winter. The advantage of leaving them in place is that the seedheads will provide food for birds.
Rose of Sharon shrub responds well to pruning. If you like, you can cut it back to within a few inches of the ground and it will resprout. In order to get a bushier effect, prune the new shoots again to make them branch.