My LL stored a lot of big folders in my apartment at the start of the lease (when I was new to USA). Could the LL allowed to do this?

Your landlord needs to remove the files or give you a rent abatement. Not only do you have less room for yourself, the presence of the files suggests that the landlord has a right to enter your apartment to access them, and that you may be held responsible if they're damaged. Take photos of the piles of files and have a conversation with the landlord. If the landlord refuses to agree to either solution you can either withhold a portion of the rent and let the landlord take you to court where you can file a counterclaim for partial lockout, or take the landlord to court for the same.