Nikita, It is always difficult to assess a situation just from what is written on the internet, but what you describe may very well be unsafe, and the apartment manager may have good grounds for asking for changes. Apologies in advance if I sound tough, but you have to be realistic to protect yourself.
First, corrugated cardboard is a favorite bedding of cockroaches. And by the time you see a cockroach, it is estimated that there are at least one hundred in the walls out of sight. Are your boxed uncorrugated? Or could you switch to uncorrugated? There is a lot of relatively inexpensive shelving/storage available. And it is fairly easy to put together stuff from throwaways that look half decent.
And depending on the age of the electrical system in your building, sticking too many items into one socket, especially in a standard extension cord, surrounded by lots of paper, is a fire hazard. It would be good to invest in a power strip that has some surge protection. This would bring the outlets within easier reach, so you could plug and unplug more easily.