1. Question: Why do the poskim say you are allowed to sell chometz with just money even though there is an argument whether you can even use money as a means of acquisition with a non-Jew or do you need to actually have him pick it up or push it, and since this is a money question and there is a question if money even works then chazaka should say that the food still belongs to the Jew and he is definitely violating owning chometz on Pesach?
A. The question of whether acquisition with money works with a non-Jew can be treated leniently in this case since the whole question is whether the food can be used after Pesach which is only a rabbinic issue since chometz left over Pesach is only prohibited after Pesach as a rabbinic fine. The problem is that this might not even be a question is the chezkas mamon can answer the question.
B. The gemara in the beginning of Pesachim says there are two things which don’t belong to a person but the Torah makes it as if it’s in your possession: Chometz found in your place on Pesach though the Torah nullifies it and a pit in the street if you undug it or opened it. The Torah just makes chometz in your possession yours in order to give you a prohibition of chometz on Pesach but you don’t actually own it.
C. The Pnei Yehoshua views the assumption of ownership for the original owner (chezkas Marie kamma) similar to the original assumed state of prohibition (chazaka dimi’ikara).
Answer: Chazaka dimi’ikara wouldn’t apply in this case because because the chometz is really taken out of your possession by the Torah on Pesach and the question is if it is put back in your possession as a new status, not as the original status or not, therefore we can be lenient and say it was in fact validly sold to the non-Jew and never went into your possession over Pesach.