Plasma and magnetic field

I was reading about plasma the other day, and I was really impressed how it interacts with magnetic field. Reasons as to why it behaves the way it does were clearly explained, but I ran into a couple of problems:

If there is a magnetic field inside plasma, compressing plasma also compresses field lines of the magnetic field. If there is no magnetic field present in plasma, moving the plasma towards a magnetic field results in field lines moving out of plasma's way.
Now, how can a magnetic field be created in plasma, as it (outside of a field) pushes the field away? And if there is a magnetic field in plasma, what would happen if somebody started to pull plasma outwards of the field? Would the magnetic field expand forever or would at some point exist plasma and return to its original position?

The magnetic polarisation is a property inherent to plasmas. As electrons are stripped away, the protons that compose the plasma are left with their positive charge and no electrons to provide a blancing negative charge. Place it in the presence of another positive charge, and the two repel one another.

Thank you for your answer. I've understood that plasma is essentially just loose nuclei (positive ions) and electrons with negative charge (and of course some neutral atoms).

But if there is originally no magnetic field inside the plasma, how can field be generated inside it? Moving a ball of plasma into a magnetic field pushes the field lines aside. Externally generated magnetic field propagetes at a finite speed (speed of light), and when it approaches the magnetically neutral ball of plasma, wouldn't it also be deformed as in the case of moving the plasma into the field?

Now say we have somehow generated the field into the plasma. Now dragging the plasma results in the field lines being dragged along the ball of plasma. Will the field lines follow plasma forever or is there some force that 'pulls' the field lines towards their orinal position, that is, will the field lines at some point let go of plasma and return to their original positions?