Is it permissible for a young man to take his agreed-upon due from the shop's money without its owner's knowledge, given that the owner did not adhere to the agreed-upon monthly increases and those in Ramadan?

It is permissible to take from the debtor's property to satisfy a right if obtaining it is impossible except through that method. This issue is known as "Mas'alat al-Zafar" (the issue of gaining access), and there is a difference of opinion among scholars regarding its permissibility.