Is it permissible for me to partner with a customer to buy and manufacture goods for the store I manage, knowing that this will not affect my work and that the price at which I buy and sell will be the market price? And does the ruling differ if I have a percentage of the store or a monthly salary?

Managing the shop requires you to be an agent for its owner. An agent is not permitted to buy or sell for himself concerning what he has been appointed for, except with permission. Otherwise, the sale or purchase would not be valid due to suspicion and the conflict with the principal's objective of maximizing profit. Therefore, your participation with a customer in buying or selling from the shop you manage is not permissible except with the shop owner's permission.