While one wants to do prapatti, should that person need to follow proper conduct like maintaining purity (madi and acaram)? As adiyen is aware that prapatti can be done at any time or place; Draupadi was in a different position when she rendered prapatti; so does that mean prapatti does not require complete acaram?

Madi, acaram are not required components of prapatti; but one should not do it without taking bath or when they are tainted with theetu; only under exceptional circumstances one can do so.

As this is a religious ceremony, one should cleanse properly, wear proper attire, and adorn twelve thirumann to perform prapatti.

Though it can be performed with theetu, does not imply it should be done with theetu.