another attempt at code golf

I had another lazy weekend go at code golf, trying to code in the most condensed way the following task. Provided with a square matrix A of positive integers, keep iterating the steps

• take the highest square 𝑥² in A.
• find the smallest adjacent neighbour 𝑛
• replace x² with x and n with nx

until no square is left (with neighbour defined as either horizontally or vertically and without wrapping around). While I managed a 217 bytes solution, compared with Robin’s 179b improvement, which remains surprising readable!, the puzzle offers two further questions:

1. is there a non-iterative way to find the final matrix B?
2. the puzzle assumes that A satisfies that at each step, the highest square x² and the smallest neighbour n will be unique, and that the sequence will not repeat forever. Is there a fool-proof way to check this is the case?