Is it permissible to borrow from someone with or without an agreement to lend to him later, in a way that both parties benefit from the loan by the same percentage, whether it be in money, gold, real estate, or a dairy cow?

It is not permissible to lend money to a person on the condition that he lends you money in return, because the Shariah has prohibited every loan that brings a benefit to the lender, based on the saying of the Prophet, peace be upon him: "Every loan that draws a benefit is usury (riba)." What is mentioned in the question is exactly "lend me and I will lend you," which is one of the major forms of usury if it is based on a condition or prior agreement. However, if there is no condition or prior agreement, then there is no harm in it.