Mutually non-congruent inscribed triangles in a polygon

We add some more to this mathoverflow post on convex polygons - and general convex regions - that have multiple least area (and least perimeter) circumscribed triangles.
------
First a couple more of questions - now on inscribed triangles.

1. What could be said on the existence of convex regions with more than 1 (or a specified n) max area inscribed triangles - all mutually non-congruent?

2. What about there being a specified number of max perimeter inscribed triangle, all mutually non-congruent?
------
One could go further and ask:
3. Are there convex regions with multiple (a specified number of ), mutually non-congruent circumscribed triangles that minimise both area and perimeter?

4. Are there convex regions with multiple and mutually non-congruent inscribed triangles that maximise both area and perimeter?