I am not a solar physicist but I believe the answere to be "Yes, there is an intinmate relationship between a star's magnetic field and its chromospheric emissions." The sun's chromosphere is virtually a seething froth of magnetically induced phenomena with filaments, flares, and underling sunspots. If it is available to you check out "SuspiciousObserver.org" on YouTube. It braodcasts daily what is happening in the solar atmosphere. I don't fully agree with the science that is reported but the photos are worth viewing!
Yes, indeed. Magnetic fields play important role in heating the chromosphere and the corona of the Sun and the magnetically active stars as well. For a comprehensive review you may visit e.g.: