On comparing Planar Convex Regions

This post is based on this old post: https://nandacumar.blogspot.com/2012/11/maximizing-and-minimizing-diameter-ii.html

Given two planar convex regions C1 and C2 both with unit perimeter, we define the difference between C1 and C2 as the least value of Hausdorff distance between C1 and C2 can have when the regions are placed above one another and adjusted to minimise the Hausdorff distance between them

Questions:

1. What are the specific pair of unit perimeter regions {C1,C2} with some equal specified area such that the difference between C1 and C2 is maximum?

2. What are the specific pair of unit perimeter regions {C1,C2} with equal specified area and equal specified diameter (diameter of a region is the greatest distance between any two points in the region). such that the difference between C1 and C2 is maximum?

These questions have been posted at https://mathoverflow.net/questions/357124/on-comparing-planar-convex-regions-of-equal-perimeter-and-area