Inside out dissections - contd.

This post continues not an earlier post here but a query posted at mathoverflow in June 2021: https://mathoverflow.net/questions/394823/further-queries-on-inside-out-polygonal-dissections
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Earlier Definitions (https://mathoverflow.net/questions/186332/inside-out-polygonal-dissections): a polygon P has an *inside out dissection* into P' if P′ is congruent to P and the perimeter of P becomes interior to P' and so the perimeter of P'is composed of internal cuts in the dissection of P. The dissection to P' is *totally inside out* (https://mathoverflow.net/questions/394823/further-queries-on-inside-out-polygonal-dissections) if we further insist that no point on the boundary of P should be on the boundary of P'. These definitions have natural analogs in 3D.
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Let us drop the requirement that the final polygon (or solid) P' be congruent to P but only insist on the inside-out (or totally inside out) nature of the dissection of P into P'.

Question 1: Given a convex polygonal region, will it always have an inside out dissection into *some* convex polygonal region? If the answer is yes (as seems to be the case), how does one achieve such a dissection with least number of intermediate pieces (thse pieces could be nonconvex but ought to be simple polygons)? If the answer is no, how does one decide whether a given polygonal region has such a dissection?
Question 1A: same question as 1 with the'fully inside out' requirement.

For an inside out (totally inside out) dissection from P to P' (both convex), is the intermediate pieces being allowed to be non-convex of any consequence? Guess: for fully inside out dissection it might be.

Question 2: Given a cube, what is the convex solid into which it can be dissected inside out with the least number of intermediate pieces?

Note: A cube can be dissected inside out via 8 smaller cubes. What we ask is if the cube can be dissected inside out into some other convex solid via less number of intermediate pieces.

Question 2A: same question as 2 with the'fully inside out' requirement.

Question 3:How does one dissect a circular disk (spherical ball) inside out into a square (cube) of same area(volume)? this question has a negative answer in the Tarski circle squaring, as given in Wiki - even a general dissection of circle to square via a finite number of pieces is impossible.

Question 4: Can one think of a analogs of the Dehn invariant to determine if two polyhedra can be inside out/ fully inside out dissected into each other?