You seem to be talking about the USSR... Which was not communist in any way, shape or form.

Communism is a stateless, classless, and moneyless society.

Guess what the USSR had?

A totalitarian state, a brutally strong class system, and money.

It was, by definition, not communist.

At best, they were a society in the socialist stage of development, according to Marx's historical materialism.

At worst, and what most anarchists and pure Marxists would argue; they were state capitalist with the capitalist class and the ruling class being one in the same, as opposed to how it is in most free-market capitalist countries where they merely have a great deal of connections between them.

The only problem you listed that could really apply was the first, but the reason you considered it a problem wouldn't apply.

To understand what communists, and socialists in general, mean when they say they oppose private property, you need to keep in mind the distinction between personal property and private property.

Personal property is property used and/or occupied by the owner.

Private property is property that is neither used nor occupied by the owner.

Thus your living space is personal property, but a restaurant is private property.

When multiple people use/occupy something, then, under personal property, they would all own it collectively. So you and your roommates would own your home and you and your coworkers would own your workplace. We oppose private property, but not personal property. In communism, you would own the field you worked or your house. However, no one could ever own a field and have others work it for them.

Having others labor for you would be capitalism.

This, by the way, is why many consider the USSR to be state capitalist. The state owned what others labored for, just as the capitalists do in free-market capitalism.

tl;dr You critiqued state capitalism, not communism.

It's a common mistake thanks to the USSR's deafening propaganda.