Problem with steering on one side only

I have been using this car for one year now and I visited some workshops, but they could not figure out the cause of the problem. I bought this car from a person, and few days later I noticed a strange behavior of the steering. When I turn the steering wheel max to the left, it does not come back to center. The steering wheel stays in that position and the car turns with jerks. However, if I turn the steering wheel to the right then everything is normal and the it goes back to the center.
Moreover, the steering does not seems to to be very stable on bumps. I feel like the steering wheel becomes slightly free-moving. While normally, the steering should continue in stable non-free-moving way even on bumps.
In addition, there is a problem similar to the alignment problem that the car pulls to one direction when I drive and the steering wheel in the center position. But it not alignment problem according to the workshop. In contrast to alignment problem, the problem I have is not consistent with one direction. That is, sometimes the car pulls to the left and other times it pulls to the right side!
Can you recognize the problem and advise how to solve it?

Thanks