Can plasma retain a magnetic field? even for the tiniest fraction of a second? If I subject plasma to a magnetic field, can it retain that field after the magnetic field suddenly ceases(the magnetic field disappears is a planck second)
for even the tiniest fraction of a second is the plasma "ferromagnetic"?
 A: The magnetic field in a conductor (such as a plasma) obeys a version of the diffusion equation:
$$
\frac{1}{\mu_0 \sigma} \nabla^2 \vec{B} = \frac{\partial \vec{B}}{\partial t}
$$
where we have assumed negligible magnetic susceptibility ($\mu \approx \mu_0$) and uniform conductivity $\sigma$.  This means that if we create a magnetic field in some region of a plasma, it will eventually decay away, just like a solute concentrated in a small part of a fluid will eventually spread out and reduce its concentration to practically zero.  
This does not happen instantaneously, though;  the time scale on which this occurs is on the order of
$$
\tau \approx \mu_0 \sigma L^2,
$$
where $L$ is the approximate size of the region of magnetic field non-uniformity.  We can see that the larger the conductivity is, or the larger the region of non-uniform magnetic field, the longer the field will last;  but eventually it will decay away.
Finally: while this time scale for demagnetization can be quite long, and so the plasma can behave a little like a ferromagnet in that regard, it is not what I (or most physicists, I think) would refer to as proper ferromagnetism.  In particular, the behavior of a magnetic field in a plasma can be described entirely classically, is largely due to the large-scale motion of charges, and does not change radically when plasma gets too hot.  None of the above statements are true of ferromagnets.
